Thread: Series

Hello, I really need a solution to this problem. My set is due tomorrow.

/sum_{k=1}^(infinity) 1/(n(n+2)
Determine whether the above series is convergent or divergent. If it is convergent, find its sum.

Thank you in advance

Originally Posted by Recklessid

Hello, I really need a solution to this problem. My set is due tomorrow.

/sum_{k=1}^(infinity) 1/(n(n+2)
Determine whether the above series is convergent or divergent. If it is convergent, find its sum.

Thank you in advance

Is this supposed to be:
sum{k = 1 to infinity} of 1/(k(k + 2)) ?

-Dan

Originally Posted by Recklessid

Hello, I really need a solution to this problem. My set is due tomorrow.

/sum_{k=1}^(infinity) 1/(n(n+2)
Determine whether the above series is convergent or divergent. If it is convergent, find its sum.

Thank you in advance

This series is convergent.

1/n(n+2) = .5/n - .5/(n+2)

This is a telescoping series.