About Chinese and Mathematics in Senior One.

Brief introduction of post-attributive in classical Chinese: in modern Chinese, attributive is used to modify and limit nouns, and it is usually placed before the head word. This word order is consistent from ancient times to the present. In classical Chinese, in addition to this situation, it can also be placed after the head word. Attribute is placed after the head word and ends with "zhe", forming the form of attribute postposition. Then when translating, we should pay attention to putting the post-attribute before the head word for translation. Method:

Format: Headword+Attributive+Zhe

(1) Help seekers can report to Qin. (Biography of Lian Po and Lin Xiangru)

Find someone who can give Qin back to me.

(2) Chu people involved in rivers. ("Carving a boat for a sword")

There is a man crossing the river in Chu State.

(3) Jingzhou people are attached to operators. (Battle of Red Cliffs)

Jingzhou belongs to Shu Ren of Cao Cao.

People from all directions came. ("Goujian Destroys Wu")

Scholars who came to Wu from all directions.

(5) Young busybodies in the village. (Donkey in Guizhou)

There is a nosy young man in the village.

2. Format: Headword+Zhi+Attribute+Zhe

(1) takes the lead. (Ma Shuo)

Translation: Maxima.

(2) Rich monks can't come.

Rich monks can't arrive.

(3) National vagrants. ("Goujian Destroys Wu")

Young people travel in the kingdom of Wu.

(4) The stone is loud and clear. (The Story of Shi Zhongshan)

A loud stone.

Format: Central Sentence+Zhi+Attribute

(1) Earthworms don't have the advantages of minions, but their bones and muscles are strong. ("Persuade to Learn")

Earthworms have no sharp claws and strong bones and muscles.

(2) According to the temple, if you are high, you will worry about your people, and if you are far away, you will worry about your king. (The Story of Yueyang Tower)

Being an official in the imperial court (or living in a high temple) means worrying about the sufferings of ordinary people, and retiring from the imperial court (or living in a distant Jianghu) means worrying about the monarch.

Format: head+ and +attribute+

(1) How many people in the world are unwilling to succeed? (Inscription of Five Tombs)

How many officials in the world can not change their ambitions?

Fifth, numerals are used as attributes after the head words.

Format: prefix+quantity attribute

(1) Compared with Chen, he rode six or seven hundred cars, rode more than one thousand, and killed tens of thousands of people.

By the time of Chen, there were six or seven hundred cars, more than one thousand cavalry and tens of thousands of soldiers.

(2) Eat all the corn and stones at once. (Ma Shuo)

Sometimes you can eat a stone of grain.

Excerpt from: Complete Interpretation of Textbooks Required 3

definition

postpositive attributive

It can be used as an attribute, a modifier and a descriptive noun in a sentence, as well as a predicative and an object complement. When adjectives are used as attributes to modify nouns, they are usually placed before the modified nouns, which is called prepositional attributes. But sometimes it can be placed after the modified noun, which is called post-attribute.

Preposition object summary In classical Chinese, the object of a verb or preposition is usually placed after the verb or preposition, but under certain conditions, the object will be placed before it. The conditions are as follows: 1. In interrogative sentences, interrogative pronouns are used as objects and prepositional objects. In this kind of sentence, the object of a preposition is also a preposition. Such as: "Is Pei Hongan there?" The key of this kind of sentence is interrogative pronouns (such as who, he, die, Hu, evil, An, Yan, etc. It is worth noting that the object of the preposition "one" is active, even if it is not an interrogative pronoun, it can be prepositioned. For example, "the rest is to remember it and let people who observe it get it." (Liu Zongyuan's Snake Catcher) The word "yes" is a general pronoun, but it is also a preposition. Second, in classical Chinese negative sentences, pronouns are used as objects and prepositions are used as objects. There are two points to pay attention to in this kind of sentence. One is negative sentences (there must be negative words such as "nothing", "nothing", "nothing", "nothing" and "nothing" in general sentences); Second, pronouns are used as objects. For example, "it is impossible for people to make promises." (Chen Shou's Biography of the Three Kingdoms and Zhuge Liang) The normal word order should be "It is impossible for people to make promises." Third, put the object before the verb with "zhi" or "yes" to emphasize the object. At this time, "zhi" is only a symbol of prepositional object, and it has no real meaning. For example, "I don't know the sentence, but I don't understand it." (Han Yu's Shi Shuo) Sometimes a range adverb "Wei" can be added before the preposition object to form the format of "Wei" ... Yes ... ". Such as: "mercenary", "obedient" and so on. Fourthly, in addition to the first case, there is another case where preposition preposition objects are sometimes prepositioned when locative words and time words are used as objects; For example, "Father sits south." (Historical Records of Xiang Yu) means "Father sits facing south."

Edit various examples of prepositional objects in this paragraph.

1), interrogative preposition object-in interrogative sentences, interrogative pronouns are used as objects, and objects are usually placed before predicates. What does Yuzhou want today? (Battle of Red Cliffs) What are you trying to say? (Battle of Red Cliffs) What is the king doing here? (Hongmen Banquet) Where are the guests? (Feng Xuan Guest Meng Changjun) Where is Pei Hongan? (The Hongmen Banquet) What do you know? ("Battle of Kan") Qin is rude. Why? If the street pavilion falls, shall we return safely? Today, I want to humiliate it. Why? ("Yan Zi makes Chu") Who deceives me and the sky? (The Analects of Confucius Zi Han) I am really incompetent. Who dares to complain? ("Zuo Zhuan Cheng Gong for three years") When Wei Jun regards his son as a politician, will his son be embarrassed first? (The Analects of Confucius Lutz) 2) Preposition object of negative sentences-In negative sentences, if the pronoun is the object, then the preposition object. Ancient people were not bullied? (Shi Zhongshan Ji) and the inner city, and vice versa, a city without feeling. (Li Shuoxue enters Cai Zhou at night) There is nothing in the book. (Zhang Hengchuan) I was willing to take care of you when I was three years old. ("Storytelling") People who can be cured because of lack of people have never been heard of since ancient times. (On Accumulation and Storage) Don't lose by not knowing your friends, but by not knowing people. ("The Analects of Confucius Learn") Ju Ze said, "I don't know." (",Zeng,, Gong Xihua Sit Down") Things are turbid and we don't know much, but we turn a blind eye. ("Involved in the River") I have no deceit, I have no worries. (Zuo Zhuan Gong Xuan Fifteen Years) Every time I compare myself with Guan Zhong and Le Yi, I can't make a promise. ("Longzhongdui") 3) Preposition object of narrative sentence-Preposition object of narrative sentence is generally marked with auxiliary words such as "Zhi, Shi". What was the sin of the Song Dynasty? I don't know what to look at, but I'm confused. ("Shi Shuo") However, a feather does not lift, so it is not hard; If you don't see your salary, don't make it clear. (Qi Huan Jinwen Shi Zhi) What good is it if you throw meat at the tiger? ("Xin Ling Jun steals the charm to save Zhao") Zhuge Lu is in Nanyang, and Ting Yun Pavilion is in Xishuzi. Kong Ziyun: "What's the matter?" (Humble Room Ming) Today I don't check, but I check my oranges? (Orangeman's Words) Life is listening. Do one's bidding. God has no relatives, but virtue has attachment. Don't treat things selfishly, only good is good. ("Ten Gradually, Ten Can't Be Sparse") Why do you love danger and destroy it? ("Zuo Zhuan Xi Gong Five Years") It is impossible for people to make promises. (Chen Shou's Biography of the Three Kingdoms and Zhuge Liang is meritocratic, so I want to use it. (Cao Cao's "Seeking the Sage Order") The cock crows and stands, the well is blocked, and the horse is the leader? (Zuo Zhuan Xiang Gong fourteen years) 4) Preposition Preposition Object-Move the preposition object before the preposition to play an emphasis role. (Note: It usually appears in interrogative sentences). (Battle of Red Cliffs) But why be cautious? Wang Yue: "How do you know?" (Biography of Lian Po and Lin Xiangru) How do you know the Prince of Yan? ("Biography of Lian Po and Lin Xiangru") If you want Khan, why add it? (Biography of Su Wu) Hey, Wes, who are we going home with? (The Story of Yueyang Tower) My king has few diseases. How can he hunt? ("Zhuang Baojian Mencius") Why wait for it with one step? ("Tan Sitong") What is the deal with Baigong in succession? (Mencius on Teng Wengong) Why don't you stay in this besieged city a little longer? (Warring States Policy Zhao Ce) Those who disagree with it think about it on their backs day and night. ("Mencius on Li Lou") 5), locative preposition object Wang Xianghe and Xiang Bo sit east; Yafu sits south. ("Hongmen Banquet") Pei Gong sits in the north; Sean lies to the west. ("The Hongmen Banquet") stood in the south in an instant, and Yao Shuai led his ministers to the north.

Edit three neglected prepositional object sentences in this paragraph.

When learning classical Chinese, people often pay more attention to interrogative pronouns in interrogative sentences, and the object should be placed in front of verbs or prepositions (such as "The Hongmen Banquet": "Is Pei Gongan there?" Another example is the Biography of Lian Po and Lin Xiangru: "The king asked,' How do you know?' ), the pronoun as the object in the negative sentence should be placed in front of the verb (for example, The Story of Shi Zhongshan: "The ancients were neither arrogant nor impetuous." ), put the object before the verb with "zhi" or "yes" (such as "public loss": "What was the crime of Song?" Another example is the idiom "Obedience means Obedience"), which ignores the sentences of the following three prepositional objects.

Preposition front

First, sometimes in order to highlight the object introduced by the preposition, the object of the preposition is placed in front of the preposition (different from the preposition object of the preposition mentioned above). In this case, the prepositions "one" and "Yu" are common. For example: ① Cut bamboo and walk along the road. When you see a small pool, the water is particularly clear. The whole stone is the bottom. ("Biography, Pond Ji") 2 It is unexpected for saints to repair the ancient times. ("Five Mistakes") 3 People who disagree will think about it day and night. (Mencius on Li Lou) (4) room in anger, the city in color. The "one" in 1 means "Yong" and the object is "Shiquan". In order to highlight "",the object is placed before "Yi". The "one" in Example 2 indicates the reason, and its object is the modern word "Shi". In order to emphasize "yes", the object is also placed before "yes". In Example 3, "day and night" means "day and night" and "night" is the object of "Yi". In order to highlight "night", the object is also placed before "Yi". In Example 4, "Shi Yu" means "Yu Shi", "Shi Yu" means "Yu Shi", and "yes" and "yes" are all objects. In order to highlight "yes" and "yes", the object is placed before "Yu".

Referential adverb

Second, the demonstrative adverb "Xiang" is used as the object and preposition object. For example: ① Mixed commitment. (Yu Gong Yi Shan) ② Closer, ... but I don't know each other. (Donkey in Guizhou) 3 I have lost my gratitude and will not agree. ("Peacock flies southeast") 4 From the way of pseudo-Xu Zi, can evil rule the country? The word "Xiang" in 1 replaces "Gong Yu". The word "phase" in Example 2 replaced "it" (donkey). "You" (Jiao Zhongqing) was replaced by "Xiang" in Example 3 and "Everyone" was replaced by "Xiang" in Example 4. These "phases" are all objects. In order to emphasize "phase", the object is placed before the verb.

Prepositions indicating adverbs

Thirdly, the demonstrative adverb "Jian" is used as the object and preposition object. Ji Jun is honest or tolerant. ("Answering Sima's Suggestion") If you see it, I hope you will come soon. ("Peacock flies southeast") When a child is born in June, a loving father sees his back. ("Chen Qingbiao") (4) At the beginning, Su Qin swallowed hundreds of money from the lender as capital. And make a fortune, with one hundred gold compensation. Report everyone who has tasted virtue. The word "see" in 1 replaces "I" (Wang Anshi). Example 2 "Look" replaces "I" (Liu Lanzhi). The word "see" in Example 3 replaced "I" (Shimi). Example 4 "see" instead of "yourself" (Su Qin). These "looks" are all objects. In order to emphasize "seeing", the object is placed before the verb. This kind of prepositional object sentence can still be seen in modern Chinese. Such as "forgive me" (please forgive me), "please teach me", "please show me" (please teach me), "please tell me" and so on. The three prepositional object sentences mentioned above are common grammatical phenomena in classical Chinese, but there are no prepositions taking them as objects in general ancient Chinese grammar books, which is unfair. These three prepositional object sentences are as important as the prepositional objects in interrogative sentences, negative sentences and prepositional objects with the help of "zhi" or "yes" in general ancient Chinese grammar books, and cannot be ignored.

The general formula of (1) geometric series is: an = a 1× q (n- 1) If the general formula is converted into an = a 1/q * q n (n ∈ n *), when q >: 0, An) is a set of isolated points on the curve y = a 1/q * q x. (2) The relationship between any two terms am and an is an = am q (n-m). (3) It can be deduced from the definition of geometric series, the general term formula, the first n terms and the formula: a1an = a2an-/kl. If π n = A 1 A2 ... records an an, then π2n- 1=(an)2n- 1, π 2n+1= (an+1) 2n+1. Besides, every item is positive. On the other hand, taking any positive number c as the cardinal number and a arithmetic progression term as the exponent, a power energy is constructed, which is a geometric series. In this sense, we say that a positive geometric series and an arithmetic series are isomorphic. Properties: ① If m, n, p, q∈N* and m+n=p+q, then am an = AP AQ；; (2) In geometric series, conversely, the sum of every k term is still a geometric series. "G is the equal ratio median of A and B" and "G 2 = AB (G ≠ 0)". (5) The sum of the first n terms in the geometric series Sn = a1(1-q n)/(1-q). A 1 (q= 1) In geometric series, the first term A 1 and the common ratio q are not zero. Note: A n in the above formula represents N power of A, and geometric series is often used in life. For example, banks have a way of paying interest-compound interest. It is to add the interest and principal of the previous period together as the principal, and then calculate the interest of the next period, which is what people usually say. The formula for calculating the sum of principal and interest according to compound interest: sum of principal and interest = principal *( 1+ interest rate) deposit period.

Edit this arithmetic progression formula.

The general formula of arithmetic progression is: an=a 1+(n- 1)d or an = am+(n-m) d. The sum of the first n terms is: sn = na 1+(n- 1))/2d or sn =.

Edit this symmetrical sequence formula.

Symmetric sequence's general term formula: the total number of terms in symmetric sequence: the letter S represents the symmetric sequence term; The letter c represents the tolerance of arithmetically symmetric sequence; The let d represents that common ratio of arithmetically symmetric sequence; The letter q stands for hypothesis, and k=(s+ 1)/2.

Edit the relevant information in this paragraph.

General term solution of general sequence

Generally, there are: an=Sn-Sn- 1 (n≥2) cumulative sum (an-an-1= ... an-1-an-2 = ... A2-a1= ... Quotient-by-quotient total multiplication (for a series with unknown numbers in the quotient of the latter term and the previous term). Reduction method (transforming a sequence so that the reciprocal of the original sequence or the sum with a constant is equal to the difference or geometric series). Specifically, in arithmetic progression, there is always sn s2n-sn s3n-s2n2 (s2n-sn) = (s3n-s2n)+sn, that is, the three are arithmetic progression and geometric progression. Fixed point method of geometric series (often used in general fractional recurrence relation)

How to write the general term of special sequence?

1,2,3,4,5,6,7,8.......- an=n 1， 1/2， 1/3， 1/4， 1/5， 1/6， 1/7， 1/8......- an= 1/n 2，4，6，8， 10， 12， 14.......- an=2n 1，3，5，7，9， 1 1， 13， 15.....- an=2n- 1 - 1， 1，- 1， 1，- 1， 1，- 1， 1......- an=(- 1)^n 1，- 1， 1，- 1， 1，- 1， 1，- 1， 1......——an=(- 1)^(n+ 1) 1，0， 1，0， 1，0， 1，0 1，0， 1....-an=[(- 1)^(n+ 1)+ 1]/2 1，0，- 1，0， 1，0，- 1，0， 1，0，- 1， 0......- an=cos(n- 1)π/2=sinnπ/2 9，99，999，9999，99999，.........-an=( 10^n)- 1 1， 1 1， 1 1， 1 1 1， 1 1 1 1.......-an=[( 10^n)- 1]/9 1，4，9， 16，25，36，49， .......an=n^2 1，2，4，8， 16，32......——an=2^(n- 1)

Solution of the summation formula of the first n terms of the sequence

(1) 1. arithmetic progression: the general formula an=a 1+(n- 1)d, the first term a 1, the tolerance d, and the nth term an=ak+(n-k)d ak of an are. If A, A and B constitute arithmetic progression, then A. Then Sn = Na 1+N (n-1) D/2 = DN 2 (that is, the quadratic power of N) /2+(a 1-d/2)n has the following summation methods:/kloc. Geometric series: the general formula an = a 1 * Q (n- 1) (that is, the n- 1 power of q) a 1 is the first term, and an is the nth term An = A668. Am = a 1 * q (m- 1), then an/am = q (n-m) (1), and an = am * q (n-m) (2). If a, g and b constitute an equal proportion term, then. Sn = a1+a2+a3 ... an Sn = a1+a1* q+a1* q 2+... a1* q (n However, it is difficult to derive some questions with the following formula. This time may be directly derived from the basic formula, so I hope this formula can be understood. )Sn = a 1( 1-q N)/( 1-q)=(a 1-an * q)。 Note: Q is not equal to1; Sn=na 1 Note: q= 1 There are generally five ways to sum: 1, complete induction (that is, mathematical induction), 2- multiplication, 3- dislocation subtraction, 4- reverse summation and 5- split term elimination.