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

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

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

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

converges

Solution steps

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

Apply Alternating Series Test:

converges

= converges

\int \frac{sin ( 2 x )}{10 + cos ^{2} ( x )} d x

\frac{s + 2}{s ^{2} + 2 s + 5} \cdot \frac{1}{s}

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

\int (\frac{sin ( x )}{x})^{2} d x

y^{^{''}} - 12 y^{^{'}} + 37 y = 0, y (0) = 6, y^{^{'}} (0) = 8

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