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

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

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

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

converges

Solution steps

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

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} + 1}

Apply Series Ratio Test:

converges

= 2 converges

= converges

\frac{d}{d x} (cot (tan (x)))

y^{^{'}} = (1 - 2 x) y^{2}, y (0) = - \frac{1}{30}

\int_{0}^{8} k (8 - x)

f (x) = - 6 x^{2} + 7 x

f (x) = - 1 - 4 e^{- \frac{x}{3}}, at x = 8

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