# Series

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• May 24th 2011, 08:38 PM
Blizzardy
Series
Hi guys, got a question which I need help in:

Show that the kth term of the series
1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) +... is 2[1/k - 1/(1+k)]
Hence find the sum of the first 50 terms.

I haven't done this type of question before so I really don't know how to start... Doesn't seem like I can apply arithmetric/geometric progression to solve too...

Thanks in advance!
• May 24th 2011, 08:49 PM
TheEmptySet
Quote:

Originally Posted by Blizzardy
Hi guys, got a question which I need help in:

Show that the kth term of the series
1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) +... is 2[1/k - 1/(1+k)]
Hence find the sum of the first 50 terms.

I haven't done this type of question before so I really don't know how to start... Doesn't seem like I can apply arithmetric/geometric progression to solve too...

Thanks in advance!

Hint the denominators are the sum of the first n integers

$1+2+3+4+...n=\frac{n(n+1)}{2}$

Can you use this to rewrite the series? It wont be geometric or arithmetic but try partial fractions.