Mathematics, 30.05.2020 15:59 gabriellebarnes66
Use the ratio test to determine whether the series is convergent or divergent.2 +4/2^2 + 8/3^2 + 16/4^2 +
Answers: 2
(1)
(2)![\lim_{n \to \infty} \frac{\frac{2^{n+1}}{(n+1)^2}}{\frac{2^n}{n^2}}= \lim_{n \to \infty} \frac{(2^n2)(n^2)}{2^n(n+1)^2}\\\\\lim_{n \to \infty} \frac{2n^2}{n^2+2n+1}= \lim_{n \to \infty} \frac{2n^2}{n^2[1+\frac{2}{n}+\frac{1}{n^2}]} \\\\\lim_{n \to \infty} \frac{2}{1+\frac{2}{n}+\frac{1}{n^2}}=\frac{2}{1+0+0}=2](/tpl/images/0671/6930/662b9.png)
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Use the ratio test to determine whether the series is convergent or divergent.2 +4/2^2 + 8/3^2 + 16/...
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