# INDUCTION PROBLEM

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• October 26th 2008, 08:23 AM
NidhiS
INDUCTION PROBLEM
I have a question.This one's either really hard or really stupid(Worried)

it's an induction problem.
$(1 - 1/2^2) * (1- 1/3^2) * ....... * ( 1 - 1/n^2) = (n+1)/2n$

(Shake) been solving it since past several hours.(Wondering) but i am not getting my L.H.S = RH.S for this one.
I started with proving if p(n) then p(n+10

so L.H.S = [1 - 1/(n+1)^2] + (n+1)/2n

R.H.s = (n+2)/2(n+1).

I can't just prove them equal.(Nerd)

Please help,
• October 26th 2008, 09:10 AM
galactus
Multiply instead of adding.

Note that $\frac{(n+1)}{2n}\cdot \left(1-\frac{1}{(n+1)^{2}}\right)=\frac{n+2}{2(n+1)}$

Which it what you want to show.
• October 26th 2008, 09:14 AM
NidhiS
I think it will be multiplied though.If you take out a term from summation you know that it needs to be added to the sum of all the other terms.
• October 26th 2008, 09:16 AM
NidhiS
oh well,i didn't see that.(Speechless).thanks!