Question

Please justify whether the series converges or diverges, and find sum, if it converges. sum_(n = 1)^ oo 3/n^2

Series
ANSWERED
asked 2021-09-02
Please justify whether the series converges or diverges, and find sum, if it converges.
\(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{3}}{{n}^{{2}}}\)

Expert Answers (2)

2021-09-03

\(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{3}}{{n}^{{2}}}\)
\(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}^{{p}}}\) – if \(\displaystyle{p}{>}{1}{Z}\) – series converges, if \(\displaystyle{p}{<}{1}\), series diverges.
Therefore, series converges by p-test.

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Best answer
2021-09-23
Right answer is on photo image
3

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