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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\int \frac{1}{( - u ^{2} + u - 1 )} d u

\frac{d}{d x} (e^{c o s (x)} + cos (e^{x}))

(1 + cos^{2} (x))^{3}

(1 + x^{2}) \frac{d y}{d x} = 2 x y + 1

\frac{d}{d x} (2 x^{2} 2 - x)

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