Series Convergence Tests
Use an appropriate test to show whether each of the following series converges or diverges.
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(a)
\(\displaystyle{\sum_{n=1}^{\infty} \frac{n-2}{3n+5}}\) Solution ↗
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(b)
\(\displaystyle{\sum_{n=1}^{\infty} \frac{n^2+1}{n2^n}}\) Solution ↗
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(c)
\(\displaystyle{\sum_{n=1}^{\infty} \frac{\sqrt{n^3+1}}{2n^3+3n^2+2}}\) Solution ↗
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(d)
\( \displaystyle{\sum_{n=0}^{\infty} \frac{(-3)^{n+1}}{2^{3n}}}\) Solution ↗
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(e)
\( \displaystyle{\sum_{n=0}^{\infty} \frac{n!}{2\cdot 5\cdot8\cdots(3n+2)}}\) Solution ↗
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(f)
\( \displaystyle{\sum_{n=2}^{\infty} \frac{1}{n\, \sqrt{\ln (n)}}}\) Solution ↗
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(g)
\(\displaystyle{ \sum_{n=1}^{\infty} \frac{(n+1)3^n}{n^32^n}}\) Solution ↗
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(h)
\(\displaystyle{\sum_{n=0}^{\infty}\left(\frac{2n^2}{3n^2+n+10}\right)^n}\) Solution ↗
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(i)
\(\displaystyle{\sum_{n=0}^{\infty}\frac{3^n\,n^2}{n!}}\) Solution ↗
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(j)
\(\displaystyle{\sum_{n=0}^{\infty}\left(\frac{n}{n+1}\right)^{n^2}}\) Solution ↗
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(k)
\(\displaystyle{\sum_{n=2}^{\infty} \frac{\ln n}{n^2}}\) Solution ↗