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 y}{d x} = 3 + e^{(- 3 x + y + 4)}

\frac{\partial}{\partial x} (x^{2} + x y^{3})

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

\frac{d}{d x} (- \frac{1}{sin ( x )})

y^{^{''}} + 3 y^{^{'}} = sin (t), y (0) = 1, y^{^{'}} (0) = 2

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