Question
Find the radius of convergence and the interval of convergence of the power series.$$\sum_{n=0}^{\infty} \frac{(-2 x)^{2 n}}{4^{n}(n+1)}$$
Step 1
Step 1: First, we rewrite the power series as follows: $$\sum_{n=0}^{\infty} \frac{(-2 x)^{2 n}}{4^{n}(n+1)} = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2 n}}{(2^n)(n+1)}$$ This simplifies the series and makes it easier to work with. Show more…
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