1. ## Test Convergence

Test the convergence of the series
$\frac{x^2}{3\sqrt{2}}+\frac{x^4}{4\sqrt{3}}+\frac{ x^6}{5\sqrt{4}}+...$

2. Originally Posted by varunnayudu
Test the convergence of the series
$\frac{x^2}{3\sqrt{2}}+\frac{x^4}{4\sqrt{3}}+\frac{ x^6}{5\sqrt{4}}+...$
$a_n = \frac{x^{2n}}{(n+2)\sqrt{n+1}}$.

Now apply the ratio test to get the radius of convergence. To check convergence at the endpoints I'd suggest using the comparison test.

3. This is an even function --> It's enough on [0, inf] to test.

divide this interval to [0, 1), [1], (1, inf] and test separatting.