What is the sum from n=1 to infinity of (5n)/(2^n) ?

The sum from n=1 to infinity of (5n)/(2^n) is converges

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sum from n=1 to infinity of (5n)/(2^n)

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

converges

Solution steps

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

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

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

Apply Series Ratio Test:

converges

= 5 converges

= converges

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

n = 0 \sum \infty \frac{n}{9 n + 1}

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

n = 0 \sum \infty \frac{3 ^{n}}{7 ^{n}}

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

What is the sum from n=1 to infinity of (5n)/(2^n) ?
The sum from n=1 to infinity of (5n)/(2^n) is converges