Question: "Classify the following series: 1+14+19+116+125+…" - Plainmath

Kyran Hudson

Answered question

2021-08-18

Classify the following series:

1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \frac{1}{25} + \dots

Answer & Explanation

liingliing8

Skilled2021-08-19Added 95 answers

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}^{\infty} \frac{1}{{(n)}^{2}}

Harmonic series are given as:

\sum_{n = 1}^{\infty} \frac{1}{{(n)}^{p}}

, in the above series p = 2
Hence, the series would be classified as a p-series with p > 1

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