How do I find the sum of this?

I got the sum of 2/3 ^n because its a Geometric sequence.

But the other part is tricky. I separated into two partial fractions but am stuck.Attachment 28824

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- Jul 14th 2013, 06:59 AMminneola24Sum of convergent series
How do I find the sum of this?

I got the sum of 2/3 ^n because its a Geometric sequence.

But the other part is tricky. I separated into two partial fractions but am stuck.Attachment 28824 - Jul 14th 2013, 07:34 AMPlatoRe: Sum of convergent series
That is a collapsing sum: $\displaystyle \sum\limits_{n = 1}^\infty {\left( {\frac{1}{{(n + 1)(n + 2)}}} \right)} = \sum\limits_{n = 1}^\infty {\left( {\frac{1}{{(n + 1)}} - \frac{1}{{(n + 2)}}} \right)} $

Any partial sum looks like $\displaystyle {S_K} = \sum\limits_{n = 1}^N {\left( {\frac{1}{{(n + 1)}} - \frac{1}{{(n + 2)}}} \right)} = \frac{1}{2} - \frac{1}{{N + 2}}$ thus $\displaystyle \left(S_N\right)\to~?$. - Jul 14th 2013, 07:44 AMminneola24Re: Sum of convergent series
How did you get to .5-1/(n+1)?

How do i complete this partial sum?

Thanks - Jul 14th 2013, 07:53 AMPlatoRe: Sum of convergent series
Do you know what it actually means for a infinite series to converge?

What do partial sums have to do with?

Do you understand how $\displaystyle {S_N} = \sum\limits_{n = 1}^N {\left( {\frac{1}{{(n + 1)}} - \frac{1}{{(n + 2)}}} \right)} = \frac{1}{2} - \frac{1}{{N + 2}}$ actually works?

If not, there is no point in your trying the question.