College Entrance Mathematics series_ limits_ mathematical induction mathematical limit

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					College Entrance Mathematics series, limit, mathematical induction mathematical limit

 series of mathematical limit induction

 Mathematical Examination series, limit, mathematical induction

 series , limits, mathematical induction

 content of the examination series. arithmetic sequences and general formulas. arithmetic
sequences and formulas before the n items. geometric sequence and the general formulas.
geometric sequence before the n items and formulas.
 series of limits and arithmetic.
 mathematical induction and its application.
 Examination requested
 (1) understand the series of related concepts. about recurrence formula is given a series of
methods, and can write a recursive formula according to the first few series.
 (2) understand the concept of arithmetic progression. mastered arithmetic progression with a
general formula of n items and formula, and can use them to solve some problems.
 (3) understand the concept of geometric series. grasp the geometric sequence with a general
formula of n items and formulas, and can use them to solve some problems.
 (4) to understand the significance of sequence limits. grasp the limits of the four algorithms, the
absolute value will be seek common ratio is less than an infinite geometric sequence and the limit
before the n items.
 (5) understand the mathematical induction principle, and be able to prove some simple
mathematical induction problems.

 review of the proposed contents of the stresses, including series, limits and mathematical
induction three-part
 1. the knowledge series Points:
 (1) understand the sequence of definition, representation, series category. understand the series is
a special function series is defined in the natural number set n (or its limited subset of (1,2,3, ... ,
n, ...)) the function f (n), when the independent variable from small to large order of values
corresponding to a time function value: f (1), f (2), f (3), ..., f (n ), .... series of images by a group
consisting of isolated points.
 (2) general term for the series formula to master: ① datum out of the general term formula, you
can find the series of the ; ② According to the first few series, write a series of general term
formula, which is a difficulty in learning to observe the series of changes to its serial number,
decomposition of the given series, the first of several, see look at the number of decomposition.
what part of the change, which is constant, then explore the change of the contact part and serial
number to summarize the law constitute a series, to write general formulas; ③ a series recursive
formula can also be used to represent; ④ (an) in the series, the first n items and an sn and the
relationship between the general term formula is a focus of this chapter, we must carefully control
the. that is an =. particular note is If a1 suitable for an = sn-sn-1 (n ≥ 2) the availability of
expression, is an expression of segmentation and do not form, can be a formula of unification.
  2. arithmetic progression of knowledge Points:
  (1) master arithmetic progression defined an +1- an = d (constant) (nn), which is a series that is
the basis of arithmetic progression, to prevent certain items from the former only if a3 -a2 = a2-a1
= d (constant) says that (an) is the arithmetic progression such errors, to judge whether a series is
arithmetic sequence. but also by the an + an +2 = 2an +1 that is an +2- an +1 = an +1- an judge.
  (2) the general term arithmetic progression as an = a1 + (n-1) d. can be organized into an = an +
(a1-d), when d ≠ 0, an is a type of n, its image is a straight line, then the point n to the set of
natural numbers.
  (3) for a is a, b of the arithmetic of items, can be expressed into 2a = a + b.
  (4) arithmetic progression and the first n items of the formula sn = · n-na1 + d, can be organized
  sn = n2 +. When d ≠ 0 when n a constant 0 of the second type.
  3. geometric series of knowledge elements: (analog arithmetic progression can learn)
  (1) to grasp the definition of geometric series = q (constant) ( nn), also prove that a sequence is a
geometric series basis. also be an · an +2 = to judge.
  (2) geometric series of general term formula an = a1 · qn-1.
  (3) for g is a, b of the arithmetic in the item, then g2 = ab, g = ±.
  (4) with particular attention to pre-geometric series formula of n items and should be divided into
q = 1 and q ≠ 1 categories.
  when q = 1 时, sn = na1.
  when q ≠ 1 时, sn =, sn =.
  (5) for the series summation. several ways to master the following key:
  ① summation of the direct use of formula;
  ② discount items grouped summation;
  ③ reverse additive summation;
  ④ wrong item subtraction sum method;
  ⑤ discount item cancellation summation.
  4. Number Limit of knowledge elements:
  (1) should have a series of limit definition: For the series (an), If there is a constant a, no matter
how small, pre-specified positive number e, can be found in a series an, so n> n when, |
an-a | <e permanent establishment, then an = a, will use this definition that a simple series
  (2) should understand the limits of algorithms. If an = a, bn = b, then the
  (an ± bn) = a ± b;
  (anbn ) = a · b;
  = (b ≠ 0).
  (3) when | q | <1, the infinite geometric sequence number and s = sn =.
  5. Knowledge of mathematical induction elements:
  should be understood as a recursive method of mathematical induction, it said the two steps. The
first step is the basis of recurrence, the second step is a recursive basis. lack of a two-step not. The
key is the second step deduction must be reasonable to use induction hypothesis.
  should focus on control guess proof, conjecture is not entirely induction conclusion, then
mathematical induction to prove that the creation of the formation of a complete process.
  Number Limit Exercises of mathematical induction,
 (1) set 2a = 3,2 b = 6,2 c = 12, the number of columns a, b, c ( )
 a. is the arithmetic progression rather than a geometric sequence
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