What is the sum from n=1 to infinity of 1/((n)^2) ?

The sum from n=1 to infinity of 1/((n)^2) is converges

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sum from n=1 to infinity of 1/((n)^2)

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

converges

Solution steps

n = 1 \sum \infty \frac{1}{n ^{2}}

Apply p-Series Test:

converges

= converges

n = 0 \sum \infty \frac{9}{5 ^{n}}

n = 1 \sum \infty (- \frac{1}{2})^{n + 3}

n = 1 \sum \infty \frac{2 n}{1 + n ^{2}}

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

k = 4 \sum \infty \frac{6}{k} - \frac{6}{k + 1}

What is the sum from n=1 to infinity of 1/((n)^2) ?
The sum from n=1 to infinity of 1/((n)^2) is converges