Telescoping series with 1/n^a - 1/(n+1)^a

[knv]

Series -- convergent or divergent?

1. Determine whether the following series is convergent or divergent. When a series is convergent, find the sum. If it diverges, find if it is infinity, - inf, or DNE.

Ʃ [(1/n^a) - 1/ (n+1)^a]




2. we are finding if a >0



3. I know that it converges but I do not know how to find the sum of it. Can anyone help me? At least get me going in the right direction

 

[w4k4b4lool4]

why don't you try redefining the summation variable in ONE of the two terms ...
what would a wise choice be?

 

[tiny-tim]

hi knv!

I know that it converges but I do not know how to find the sum of it.

try writing out the sum of the first three or four terms …

do you see a pattern? ​