What is the sum from n=1 to infinity of 2/(3^n+20) ?

The sum from n=1 to infinity of 2/(3^n+20) is converges

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sum from n=1 to infinity of 2/(3^n+20)

n = 1 \sum \infty \frac{2}{3 ^{n} + 20}

converges

Solution steps

n = 1 \sum \infty \frac{2}{3 ^{n} + 20}

Apply the constant multiplication rule:

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

= 2 \cdot n = 1 \sum \infty \frac{1}{3 ^{n} + 20}

Apply Series Ratio Test:

converges

= 2 converges

= converges

n = 1 \sum \infty \frac{7}{n ^{2} + n}

i = 1 \sum \infty 5 \cdot i

n = 1 \sum \infty n^{- 1 - \frac{1}{n}}

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

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

What is the sum from n=1 to infinity of 2/(3^n+20) ?
The sum from n=1 to infinity of 2/(3^n+20) is converges