I need to evaluate this for convergence/divergence:
I tried a Limit Comparison Test with in the denominator, but that didn't get me anywhere. I don't see another function to compare this to.
Can anybody suggest what I might try?
Thanks.
Hello, joatmon!
I need to evaluate this for convergence/divergence:
. .
For , we have: . .[1]
We have: .
. . Then: . .[2]
Multiply [1] and [2]: .
. . . . . . . . We have: . . . . . . .
Hence: .
The given series is less than a convergent p-series.
. . Therefore, it converges.
Well done. Thanks!
I was thinking about this a little more and I think that TKHunny's solution doesn't quite work because the final comparative function is not quite a p-series, so it doesn't definitively establish the original function as convergent. Then I saw Soroban's effort, and now I see how to get there.
Thanks to both of you!