Hello

Problem:

For which positive integer k is the following series convergent?

The Ratio Test seems a good choice.

After applying the Ratio Test, I will face the following limit:

Then ?

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- January 16th 2010, 04:33 PMGeneralFind value of k for which the series converges.
**Hello**

Problem:

For which positive integer k is the following series convergent?

**The Ratio Test seems a good choice.**

After applying the Ratio Test, I will face the following limit:

**Then ?** - January 16th 2010, 04:44 PMCalculus26
(kn+k)! = (kn+k)...................(kn+1)(kn)!

you have (n+1)^2/[(kn+k)...................(kn+1)

for k = 2

lim(n+1)^2/ [2(n+1)(2n+1)] = 1/4 and we have convergence

For k > 2 limit is 0 as denominator is of order 3 or higher

for k= 1 lim(n+1)^2/(n+1) = infinity