What is the sum from n=1 to infinity of 2/(5^n-4) ?

The sum from n=1 to infinity of 2/(5^n-4) is converges

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sum from n=1 to infinity of 2/(5^n-4)

n = 1 \sum \infty \frac{2}{5 ^{n} - 4}

converges

Solution steps

n = 1 \sum \infty \frac{2}{5 ^{n} - 4}

Apply the constant multiplication rule:

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

= 2 \cdot n = 1 \sum \infty \frac{1}{5 ^{n} - 4}

Apply Series Ratio Test:

converges

= 2 converges

= converges

n = 0 \sum \infty \frac{n}{7 n + 1}

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

n = 1 \sum \infty (n!) e^{- n}

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

n = 0 \sum \infty \frac{1}{7 + n}

What is the sum from n=1 to infinity of 2/(5^n-4) ?
The sum from n=1 to infinity of 2/(5^n-4) is converges