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

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

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

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply p-Series Test:

converges

= - converges

= converges

n = 1 \sum \infty \frac{2 n + 3}{n + 1}

n = 1 \sum \infty (\frac{1 + 5}{n})^{n}

n = 0 \sum \infty 2 (\frac{1}{3})^{n}

n = 1 \sum \infty \frac{17 n}{n !}

n = 9 \sum \infty \frac{n !}{n ^{n}}

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