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

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

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

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

converges

Solution steps

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

Apply Alternating Series Test:

converges

= converges

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

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

n = 2 \sum \infty \frac{3}{n ( n + 3 )}

n = 1 \sum \infty \frac{1}{n ^{2} + 30}

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

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