What is the sum from n=0 to infinity of 2(2/3)^{3n} ?

The sum from n=0 to infinity of 2(2/3)^{3n} is converges

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sum from n=0 to infinity of 2(2/3)^{3n}

n = 0 \sum \infty 2 (\frac{2}{3})^{3 n}

converges

Solution steps

n = 0 \sum \infty 2 (\frac{2}{3})^{3 n}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty (\frac{2}{3})^{3 n}

Apply Series Ratio Test:

converges

= 2 converges

= converges

\int \frac{x}{x + 1 - ( x + 1 )} d x

\frac{\partial}{\partial y} (x^{2} e^{y z^{2}})

\int_{0}^{1} x 1 - x d x

\frac{3}{2 3 x + 13}, at x = - 3

x, \frac{d ^{2} x}{d t ^{2}} + x = (t^{2} + t) sin (t)

What is the sum from n=0 to infinity of 2(2/3)^{3n} ?
The sum from n=0 to infinity of 2(2/3)^{3n} is converges