What is the sum from n=0 to infinity}5^{-2n+1 of 3^n ?

The sum from n=0 to infinity}5^{-2n+1 of 3^n is converges

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sum from n=0 to infinity}5^{-2n+1 of 3^n

n = 0 \sum \infty 5^{- 2 n + 1} 3^{n}

converges

Solution steps

n = 0 \sum \infty 5^{- 2 n + 1} \cdot 3^{n}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty n ln (1 + \frac{1}{n})

n = 1 \sum \infty 4^{3 - 3 n}

k = 1 \sum \infty \frac{k}{2 ^{k - 1}}

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

n = 1 \sum \infty \frac{1}{2 n ^{2} + n}

What is the sum from n=0 to infinity}5^{-2n+1 of 3^n ?
The sum from n=0 to infinity}5^{-2n+1 of 3^n is converges