I am stuck on this question

I tried using

Holly Guerrero
2021-12-14
Answered

The series $\sum _{n=1}^{\mathrm{\infty}}{n}^{k}{r}^{n}$ coverges when $r\in (0,1)$ and diverges when $r>1$ . This is true regardless of the value of the constant k. When $r=1$ the series is a p-series. It converges if $k<-1$ and diverges otherwise Each of the series below can be compared to a series of the form $\sum _{n=1}^{\mathrm{\infty}}{n}^{k}{r}^{n}$ . For each series determine the best value of r and decide whether the series converges.

I am stuck on this question$\sum _{n=1}^{\mathrm{\infty}}{\left(\frac{3{n}^{2}+4n+{2}^{-2n}}{{7}^{n+2}+4n+5\sqrt{n}}\right)}^{2}$

I tried using$\frac{{2}^{-2n}}{{7}^{n+2}}$ and ended up with a value of r of $\frac{1}{4\cdot 7}$ but this didn't work.

I am stuck on this question

I tried using

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