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

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

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

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

converges

Solution steps

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

Apply p-Series Test:

converges

= converges

k = 1 \sum \infty (- \frac{1}{4})^{k}

n = 1 \sum \infty \frac{n ^{4}}{3 ^{n}}

n = 0 \sum \infty \frac{7}{n ^{2} + 9}

n = 1 \sum \infty \frac{9}{n ^{2} + n ^{3}}

k = 3 \sum \infty \frac{7}{k ln ^{2} ( k )}

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