What is the sum from n=0 to infinity of 2/((-3)^n) ?

The sum from n=0 to infinity of 2/((-3)^n) is 3/2

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sum from n=0 to infinity of 2/((-3)^n)

n = 0 \sum \infty \frac{2}{( - 3 ) ^{n}}

\frac{3}{2}

Solution steps

n = 0 \sum \infty \frac{2}{( - 3 ) ^{n}}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty \frac{1}{( - 3 ) ^{n}}

Apply Series Geometric Test:

\frac{3}{4}

= 2 \cdot \frac{3}{4}

Simplify

2 \cdot \frac{3}{4} : \frac{3}{2}

= \frac{3}{2}

n = 1 \sum \infty \frac{2}{3 n - 1}

n = 2 \sum \infty \frac{- 1}{ln ( n )}

n = 3 \sum \infty \frac{7}{n} - \frac{7}{n + 2}

k = 0 \sum \infty \frac{k}{4 k + 1}

n = 0 \sum \infty \frac{n}{8 n ^{6} + 1}

What is the sum from n=0 to infinity of 2/((-3)^n) ?
The sum from n=0 to infinity of 2/((-3)^n) is 3/2