Select all correct statements for the following series A. $$ \sum_{1}^{\infty} \frac{1}{\sqrt{2n-1}} $$ B. $$ \sum_{n=1}^{\infty} \frac{1}{\ln n} $$ C. $$ \sum_{n=1}^{\infty} (-1)^{n+1} \frac{1}{\ln n} $$ D. $$ \sum_{n=1}^{\infty} a^{n} $$ where $$ 1/2 < a < 1 $$ A converges B converges C converges D converges A diverges B diverges C diverges D diverges
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Let $$ a_n = \frac{1}{\sqrt{2n-1}} $$ and $$ b_n = \frac{1}{\sqrt{n}} = \frac{1}{n^{1/2}} $$. The series $$ \sum_{n=1}^{\infty} \frac{1}{n^{1/2}} $$ is a p-series with $$ p = 1/2 \le 1 $$, so it diverges. Now, let's compute the limit: $$ \lim_{n \to \infty} Show more…
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