What is the sum from n=1 to infinity of 1/(4+3^n) ?

The sum from n=1 to infinity of 1/(4+3^n) is converges

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sum from n=1 to infinity of 1/(4+3^n)

n = 1 \sum \infty \frac{1}{4 + 3 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{1}{4 + 3 ^{n}}

Apply Series Ratio Test:

converges

= converges

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

n = 0 \sum \infty \frac{4}{9 ^{n}}

n = 0 \sum \infty \frac{n}{n ^{2} + n + 1}

n = 1 \sum \infty n (\frac{8}{9})^{n}

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

What is the sum from n=1 to infinity of 1/(4+3^n) ?
The sum from n=1 to infinity of 1/(4+3^n) is converges