Calculus Problem

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OK guys, here's my problem

find the values of P such that the series, ln (n)/n^p converges.

Im guessing p>1 is the answer but I dont know how to prove it...


help me please!

Actually, p>=1 would work too (or even possibly p>=0 (anything raised to 0 is 1).

As far as the proof, I would not remember how to state it in mathematical terms but I can say that somewhere in the answer, it should read that as p gets larger, so does the denominator and therefore the whole equation converges toward 0 (which is what the answer would be at p=infinity).

I hope this helped somewhat.

Have you had any luck with this? I was trying to solve it last night but I can't integrate with that p in the denominator.

actually, using the comparison test, I found that when p>1 the series converges because:

0<=(ln n)/n^p<=1/n^p and when p>1, 1/n^p converges and therefore the original series converges...


i think this works, but its cool cause I can loose one point on the hw. and it wasnt on my test today so its all good.