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

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

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sum from n=0 to infinity of 3^{-2n}

n = 0 \sum \infty 3^{- 2 n}

converges

Solution steps

n = 0 \sum \infty 3^{- 2 n}

Apply Series Ratio Test:

converges

= converges

\frac{d}{d x} (ln (3 x e^{- x}))

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