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

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

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

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

converges

Solution steps

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

Apply Alternating Series Test:

converges

= converges

n = 0 \sum \infty 4 (\frac{1}{2})^{n - 2}

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

n = 3 \sum \infty \frac{1}{n ^{2} - 2 n}

n = 1 \sum \infty arccos (\frac{1}{n}) - arccos (\frac{1}{n + 1})

n = 3 \sum \infty \frac{1}{4 n ^{2} - 1}

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