What is the sum from n=1 to infinity of 2(2/3)^{n-1} ?

The sum from n=1 to infinity of 2(2/3)^{n-1} is converges

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sum from n=1 to infinity of 2(2/3)^{n-1}

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Ratio Test:

converges

= 2 converges

= converges

\frac{d}{d x} (cos (x) ln (cos (x)))

\frac{d y}{d t} = 2 y + 2 t^{2} - \frac{10}{3} t

\int 2 z d z

x^{5} sin (x)

\frac{d}{d x} (\frac{sin ( x )}{cos ^{2} ( x )})

What is the sum from n=1 to infinity of 2(2/3)^{n-1} ?
The sum from n=1 to infinity of 2(2/3)^{n-1} is converges