What is the sum from n=0 to infinity of 4/(5^{n/3)} ?

The sum from n=0 to infinity of 4/(5^{n/3)} is converges

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sum from n=0 to infinity of 4/(5^{n/3)}

n = 0 \sum \infty \frac{4}{5 ^{\frac{n}{3}}}

converges

Solution steps

n = 0 \sum \infty \frac{4}{5 ^{\frac{n}{3}}}

Apply the constant multiplication rule:

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

= 4 \cdot n = 0 \sum \infty \frac{1}{5 ^{\frac{n}{3}}}

Apply Series Ratio Test:

converges

= 4 converges

= converges

n = 0 \sum \infty \frac{1}{e}

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

n = 1 \sum \infty (- \frac{3}{5})^{n - 1}

k = 0 \sum \infty (0.5)^{k}

n = 1 \sum \infty \frac{π ^{n}}{3 ^{n}}

What is the sum from n=0 to infinity of 4/(5^{n/3)} ?
The sum from n=0 to infinity of 4/(5^{n/3)} is converges