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Old 08-04-2007   #27
Sillysidley

 
Join Date: Oct 2006
Posts: 822
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Eh, close enough
The first one uses a telescoping series (basically where a bunch of things cancel out) and the second has a formula (and just to get better at proofs, I wanna prove it)
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We want all the terms except the first and last to cancel. So, we express it as:

2nd:
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There's a formula that says the sum of n numbers of this kind sum up to . In other words, We can then easily see the answer is .

Proof: Easy enough to prove by induction:
For n=1, the LHS=RHS=. Let's assume it holds for n. Then, for n+1;
And we're finally done
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Last edited by Sillysidley; 08-04-2007 at 05:06 PM..
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