What is the sum from n=1 to infinity of n(-3/7)^n ?

The sum from n=1 to infinity of n(-3/7)^n is converges

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sum from n=1 to infinity of n(-3/7)^n

n = 1 \sum \infty n (- \frac{3}{7})^{n}

converges

Solution steps

n = 1 \sum \infty n (- \frac{3}{7})^{n}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{5}{n ^{2} + 36}

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

k = 1 \sum \infty (cos (10))^{k}

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

n = 1 \sum \infty cos (\frac{16}{n})

What is the sum from n=1 to infinity of n(-3/7)^n ?
The sum from n=1 to infinity of n(-3/7)^n is converges