(a) \(\displaystyle{\sum_{n=1}^{\infty} \frac{n-2}{3n+5}}\)
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(f) \( \displaystyle{\sum_{n=2}^{\infty} \frac{1}{n\,
\sqrt{\ln (n)}}}\) solution
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(b) \(\displaystyle{\sum_{n=1}^{\infty} \frac{n^2+1}{n2^n}}\)
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(g) \(\displaystyle{ \sum_{n=1}^{\infty} \frac{(n+1)3^n}{n^32^n}}\)
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(c) \(\displaystyle{\sum_{n=1}^{\infty} \frac{\sqrt{n^3+1}}{2n^3+3n^2+2}}\)
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(h) \(\displaystyle{\sum_{n=0}^{\infty}\left(\frac{2n^2}{3n^2+n+10}\right)^n}\)
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(d) \( \displaystyle{\sum_{n=0}^{\infty} \frac{(-3)^{n+1}}{2^{3n}}}\)
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(h) \(\displaystyle{\sum_{n=0}^{\infty}\frac{3^n\,n^2}{n!}}\)
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(e) \( \displaystyle{\sum_{n=0}^{\infty} \frac{n!}{2\cdot
5\cdot8\cdots(3n+2)}}\)
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(i) \(\displaystyle{\sum_{n=0}^{\infty}\left(\frac{n}{n+1}\right)^{n^2}}\)
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(j) \(\displaystyle{\sum_{n=2}^{\infty} \frac{\ln n}{n^2}}\)
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