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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{3 ^{n}}{8 ^{n}}

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

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

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

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

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