This is the equation that i have ended up with

$\displaystyle \sum_{n=0}^{\infty} \frac{x^{2n}}{(n+2) \sqrt{n+1}}$

I am using the Ratio test $\displaystyle \frac{u_{n+1} }{u_n} = k$ ....if $\displaystyle k<1 (convergent)$ $\displaystyle k>1(divergent)$ ....

$\displaystyle \lim_{n \to \infty} \frac{u_{n+1}}{u_n}$ = $\displaystyle \lim_{n \to \infty} \frac{x^2}{n+3 \sqrt{n+2}} . \frac{n+2 \sqrt{n+1}}{1}$

= $\displaystyle x^2 \frac{n+2 \sqrt{n+1}}{n+3 \sqrt{n+2}}$ .........I am stuck here what should i do next?????