What is the sum from n=1 to infinity of n^{-2} ?

The sum from n=1 to infinity of n^{-2} is converges

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sum from n=1 to infinity of n^{-2}

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

converges

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

Apply p-Series Test:

converges

= converges

\frac{\partial}{\partial x} (5 x^{4} y^{3} + 2 x y)

y^{^{'}} + t^{2} y = 1

\int_{0}^{\infty} e^{\frac{- x ^{2}}{2}} d x

\int \frac{1}{x ^{2}} cos^{2} (\frac{1}{x}) d x

f (x) = \frac{2 x}{x}

What is the sum from n=1 to infinity of n^{-2} ?
The sum from n=1 to infinity of n^{-2} is converges