Hey, folks!

How would you calculate the sum of (k^(j + n))/(m + k)^n, where summation variable is k and k = 1 to infinity?

j, n, and m are positive integers.

Thanks in advance.

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- March 2nd 2009, 08:49 AMcuriousCalculating series...
Hey, folks!

How would you calculate the sum of (k^(j + n))/(m + k)^n, where summation variable is k and k = 1 to infinity?

j, n, and m are positive integers.

Thanks in advance. - March 2nd 2009, 09:51 AMcurious
Solved. It doesn't converge. :)

- March 2nd 2009, 10:10 AMJameson
Mind showing your solution so this thread may be useful to others later on? Otherwise it will be deleted. (Surprised)

- March 2nd 2009, 10:20 AMcurious
Well, the necessary condition for series to converge is lim a_k -> 0 as k tends to infinity.

In my case, a_k = (k^(j + n))/(m + k)^n = (k^j)*(1 - m/(m + k))^n.

As k -> infinity, (1 - m/(m + k))^n -> 1, while k^j -> infinity.

Which means a_k is unbounded. So, the necessary condition is not satisfied. - March 2nd 2009, 10:44 AMKrizalid
- March 2nd 2009, 10:47 AMMoo
- March 2nd 2009, 10:49 AMcurious
Yeah, sure. It's only the necessary condition.

That is, if a_k -> 0, it doesn't mean that the series will converge.

But if a_k -> "something other than 0", then definitely the series won't converge.