[INTERGRAL TEST] Find the values of p for which this series is convergent.

(See my subsequent post)

Question

[INTERGRAL TEST] Find the values of p for which this series is convergent.

(See my subsequent post)

anonymous · Answer

Now I hope somebody will come

anonymous · Answer

maybe by root test:
$$\sqrt[n]{1/Ln( n) ^{np}}=1/Ln (n) ^{p}<1$$
so p>1/Ln(n)

anonymous · Answer

No I have not learned root test yet

anonymous · Answer

integral test?

anonymous · Answer

Yes integral test

anonymous · Answer

Wait, I actually got the answer to this question. There is another problem that asks for the same thing but is slightly more complicated. Let me edit the first post

anonymous · Answer

attachment

anonymous · Answer

ok lets see if we can find an anti derivative
maybe try $u=\ln(x)$ so $du=\frac{dx}{x}$ and you have 
$$\int \frac{du}{u^p}=\frac{u^{p+1}}{p+1}=\frac{\ln(x)^{p+1}}{p+1}$$

anonymous · Answer

Which one are you doing?

anonymous · Answer

See my latest attachment. That is the one I really need help with

anonymous · Answer

wow those hits just keep coming
are we supposed to find an anti derivative for that thing??

anonymous · Answer

That is what I was thinking, but then I end up getting stuck when I try to evaluate the integral

anonymous · Answer

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