I need help for the following problem. Find the radius of convergence for the power series: $\displaystyle \sum_{j=1}^{\infty} (x/2)^j$
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Originally Posted by larson I need help for the following problem. Find the radius of convergence for the power series: $\displaystyle \sum_{j=1}^{\infty} (x/2)^j$ By the root test, the series converges for all $\displaystyle x$ such that $\displaystyle \lim_{j \to \infty} |(x/2)^j|^{1/j} < 1$ don't forget to check the end points
Originally Posted by Jhevon By the root test, the series converges for all $\displaystyle x$ such that $\displaystyle \lim_{j \to \infty} |(x/2)^j|^{1/j} < 1$ don't forget to check the end points how do i know what my endpoints are?
Hello, Find the radius of convergence R, then look at the convergence/divergence of the series if x=R and x=-R
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