Use the ratio test to find the interval of convergence of the following power series:
$x^{2}-\frac{x^{4}}{4}+\frac{x^{6}}{9}+\ldots+\frac{(-1)^{n+1} x^{2 n}}{n^{2}}+\ldots$

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The Answer of Use the ratio test to find the interval of convergence of the following power series:
$x^{2}-\frac{x^{4}}{4}+\frac{x^{6}}{9}+\ldots+\frac{(-1)^{n+1} x^{2 n}}{n^{2}}+\ldots$

Use the Ratio Test to Find the Interval of Convergence x2−x44+x69+…+(−1)n+1x2nn2+…x^{2}-\frac{x^{4}}{4}+\frac{x^{6}}{9}+\ldots+\frac{(-1)^{n+1} x^{2 n}}{n^{2}}+\ldotsx2−4x4​+9x6​+…+n2(−1)n+1x2n​+…

Use the Ratio Test to Find the Interval of Convergence $x^{2}-\frac{x^{4}}{4}+\frac{x^{6}}{9}+\ldots+\frac{(-1)^{n+1} x^{2 n}}{n^{2}}+\ldots$