Test the convergence of the series $\displaystyle \frac{x^2}{3\sqrt{2}}+\frac{x^4}{4\sqrt{3}}+\frac{ x^6}{5\sqrt{4}}+...$
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Originally Posted by varunnayudu Test the convergence of the series $\displaystyle \frac{x^2}{3\sqrt{2}}+\frac{x^4}{4\sqrt{3}}+\frac{ x^6}{5\sqrt{4}}+...$ $\displaystyle a_n = \frac{x^{2n}}{(n+2)\sqrt{n+1}}$. Now apply the ratio test to get the radius of convergence. To check convergence at the endpoints I'd suggest using the comparison test.
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.
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