FP1 MEI Induction and Series

For standard results I have left gaps before the equals sign as greek letters cannot be typed. From top to bottom they should be the sum of: 1, r, r^2, r^3 between r=1 and n. Where a number is below an expression such as the standard results, the expression is divided by this number. Finally, for the last standard result, the n is n^2 and the (n+1) is (n+1)^2.

I have left these blank as I prefer adding what cannot be typed in pen, after printing. Sorry if you are not printing.

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  • Created by: Chloe
  • Created on: 21-04-14 13:21
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  • Induction and Series
    • Proof by Induction
      • Step 2: Prove that if the result is true for n=k then it is true for n=k+1
        • Step 3: conclude the result is true for n>=1
      • Step 1: Prove the result is true for n=1
        • Step 2: Prove that if the result is true for n=k then it is true for n=k+1
          • Step 3: conclude the result is true for n>=1
      • Proves a general expression for the sum of a series
        • I.e. given a sum 1+2+...+n and an expression   =   n(n+1)     2
      • Given an iterative formula and a term i.e. a=2
        • Prove true for 1st term a. Prove true for (k+1)th term when true for the kth term
    • Summation of series
      • Arithmetic
        • ak=a+(k-1)d where a is 1st term and d is the common difference
        • Sum of 1st n terms:         n(2a+(n-1)d) 2
      • Geometric
        • ak=ar^(k-1) where a is 1st term and r is the common ratio
        • Sum of 1st n terms:          a(1-r^n)  (1-r)
      • Method of differences
        • Aim to split the given expression so that terms cancel
        • Questions often split apart into parts    i) show that.. ii) hence find...
      • standard results
        • =n(n+1)(2n+1) 6
        • =n(n+1)      2
        • =n (n+1)     4
        • =n

Comments

Mohammed

Very good detailed information, but I would make it clear when displaying some of the formulae properly. It can be done either by doing on paper then scanning it, or finding a programme that let's you display them properly, and screenshot that part and insert it.

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