$$ \sum_{k=1}^∞ \frac{(x^k)} {(k^2)} $$ The question is, Check if it is divergent. Solution: Step1: $$ R_1 = \frac{1}{lim \frac{k^2}{(k+1)^2}} =1 $$ can someone explain step 1.Which method is used to solve it? Is it cauchy?
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1It seems to be you're using some kind of D'Alembert's (ratio's) test: for a power series as yours, the convergence radius $;R;$ is given by $$\frac1R=\lim_{k\to\infty}\frac{a_{k+1}}{a_k}; $$and in your case with $;a_k=\frac1{k^2};$ ... – DonAntonio Mar 14 '22 at 17:49
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@DonAntonio thanks got it – FinallySignedUp2 Mar 14 '22 at 18:13