Infinite Sum (Telescoping Series): ∑ (n=1)^∞ of (2/n(n+2))

[yogabagaba93]

talk slower babe 

[komei93]

in fact the series does not converge to 3/2, you've made a mistake by omitting 2 last terms of the sum with the partial fraction n+2. Check yourself :)

[alkmaher]

To make it even clearer, I believe you should show people that one must include the limit of 1/(n+2) as n --> to infinity to show them that it'll give 0. So it won't affect the answer. I think this is important because in some cases, such as the series for ln((n+1)/(n)), the series actually diverges even though everything cancels out.

[TucsonMathDoc]

@alkmaher

good point. -MathDoc