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

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

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

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

converges

Solution steps

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

Apply Series Comparison Test:

converges

= converges

n = 1 \sum \infty (\frac{2}{9})^{n}

n = 1 \sum \infty n e^{- 16 n}

n = 1 \sum \infty (- 0.005)^{n}

n = 1 \sum \infty \frac{2}{n ln ( 9 n )}

n = 1 \sum \infty \frac{n !}{11 6 ^{n}}

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