Classify the following series: 1 + 1/4 + 1/9 + 1/16 + 1/25 + …

Kyran Hudson 2021-08-18 Answered
Classify the following series: \(\displaystyle{1}+\frac{{1}}{{4}}+\frac{{1}}{{9}}+\frac{{1}}{{16}}+\frac{{1}}{{25}}+…\)

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Expert Answer

liingliing8
Answered 2021-08-19 Author has 12132 answers
\(\displaystyle{1}+\frac{{1}}{{4}}+\frac{{1}}{{9}}+\frac{{1}}{{16}}+\frac{{1}}{{25}}+…\)
\(\displaystyle\frac{{1}}{{1}^{{2}}}+\frac{{1}}{{2}^{{2}}}+\frac{{1}}{{3}^{{2}}}+\frac{{1}}{{4}^{{2}}}+\frac{{1}}{{5}^{{2}}}+…\), so \(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{\left({n}\right)}^{{2}}}\)
Harmonic series are given as: \(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{\left({n}\right)}^{{p}}}\), in the above series p = 2
Hence, the series would be classified as a p-series with p > 1
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