Math CentralQuandaries & Queries


Question from SAMUEL, a student:
use mathematical induction to proof that each statement is true for every positve integer n


  1. Prove it's true for the first case:

    1/(1*2) = 1/(1+1)

  2. Show that if it's true for the (n-1)st case it's true for the nth case [or that if it's true for the nth case it's true for the (n+1)st case, whichever is tidier.] To do this, use the fact that

    [1/(1*2) + 1/(2*3) + ... + 1/n(n+1)] [*]
    this is the nth left-hand side

       = [1/(1*2) + 1/(2*3) + ... + 1/(n-1)n] + 1/n(n+1) [**]
       this is the (n-1)st left-hand side

SUPPOSE [1/(1*2) + 1/(2*3) + ... + 1/(n-1)n] = (n-1)/n (the "inductive hypothesis") and substitute this into [**]. Simplify to get n/n+1; you have then shown that [*] = n/n+1 as desired.

-Good Hunting!


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