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

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

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

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

converges

Solution steps

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

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

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

Apply Series Comparison Test:

converges

= 2 converges

= converges

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

\frac{1}{2 x + 3}

\frac{d}{d x} (2 + sec (x))

\frac{1}{4}

\frac{d}{d x} (arctan (3 x^{2}))

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