# Thread: Comparison test question

1. ## Comparison test question

hi everyone

need help with this question:

Use comparison test to determine the convergent of the following series:

$\displaystyle 1,\frac{1}{2^2},\frac{1}{3^3},\frac{1}{4^4}$

i found the general form,$\displaystyle \frac{1}{n^n}$ but i cant do the comparison. needhelp & guidance for this question.

really appreciate all your help & support.

2. I think it converges but I'm not sure what's the best comparison, it's already too simple. My inspection is based on a case like $\displaystyle s_n = \frac{1}{n2^n}$ for instance, when you can just compare it with $\displaystyle \sum \frac{1}{2^n}$ and you know it converges.

3. thank you for replying. just wondering how to prove it converges...stuck.

need some help on this problem.

thank you for all help & support,appreciated.

4. $\displaystyle n^n\geq n^2 \forall n>2 \implies \frac{1}{n^2}\geq \frac{1}{n^n} \forall n>2$