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

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

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sum from n=5 to infinity of (4^n)/(5^n)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{n + 6}{n ^{2}}

n = 1 \sum \infty \frac{2 n}{n ^{2} + 4}

k = 2 \sum \infty \frac{k}{ln ( k )}

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

n = 8 \sum \infty \frac{1}{n ^{2} + 64}

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