Kyran Hudson

2021-08-18

Classify the following series: $1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\dots$

liingliing8

$1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\dots$
$\frac{1}{{1}^{2}}+\frac{1}{{2}^{2}}+\frac{1}{{3}^{2}}+\frac{1}{{4}^{2}}+\frac{1}{{5}^{2}}+\dots$, so $\sum _{n=1}^{\mathrm{\infty }}\frac{1}{{\left(n\right)}^{2}}$
Harmonic series are given as: $\sum _{n=1}^{\mathrm{\infty }}\frac{1}{{\left(n\right)}^{p}}$, in the above series p = 2
Hence, the series would be classified as a p-series with p > 1

Do you have a similar question?