What is the sum from n=1 to infinity of (2n)/(11^n) ?

The sum from n=1 to infinity of (2n)/(11^n) is converges

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sum from n=1 to infinity of (2n)/(11^n)

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Ratio Test:

converges

= 2 converges

= converges

\frac{d}{d x} (\frac{4 2}{3} x^{\frac{3}{2}} - 1)

(1 - x^{\frac{2}{3}})^{\frac{3}{2}}

\int 3 x^{2} y + 4 x y^{2} d x

\int 7 tan (8 x) sec^{2} (8 x) d x

\int x + 6 d x

What is the sum from n=1 to infinity of (2n)/(11^n) ?
The sum from n=1 to infinity of (2n)/(11^n) is converges