What is the sum from n=0 to infinity of 1/((n+1)^2) ?

The sum from n=0 to infinity of 1/((n+1)^2) is converges

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sum from n=0 to infinity of 1/((n+1)^2)

n = 0 \sum \infty \frac{1}{( n + 1 ) ^{2}}

converges

Solution steps

n = 0 \sum \infty \frac{1}{( n + 1 ) ^{2}}

Apply Series Comparison Test:

converges

= converges

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

f (x) = 5 e^{x} cos (x)

\int_{- 6}^{x} 36 - t^{2} d t

(1 + x)^{\frac{1}{2}}, 0

What is the sum from n=0 to infinity of 1/((n+1)^2) ?
The sum from n=0 to infinity of 1/((n+1)^2) is converges