What is the sum from n=0 to infinity of (2n)/(2^n) ?

The sum from n=0 to infinity of (2n)/(2^n) is converges

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sum from n=0 to infinity of (2n)/(2^n)

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty \frac{n}{2 ^{n}}

Apply Series Ratio Test:

converges

= 2 converges

= converges

\int \frac{d}{1} (e^{x^{2}} y) d x

\frac{d y}{d x} = - 5 + x + y

3 7 x^{4} + 8 x^{3}

\frac{200}{0.9 + 0.1 e ^{2 h}}

\int \frac{\frac{1}{z} - x ^{2}}{x ^{2}} d x

What is the sum from n=0 to infinity of (2n)/(2^n) ?
The sum from n=0 to infinity of (2n)/(2^n) is converges