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

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

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

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

converges

Solution steps

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

Apply p-Series Test:

converges

= converges

\int e^{- 2 a x} d x

\int (\frac{x ^{2} + 2 x - 3}{x ^{4}}) d x

x = e^{y}, y = 0, x = 1, x = e^{2}

\int e^{- 2 x^{2}} x d x

\int \frac{x ^{3}}{3 x ^{2} + 7} d x

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