What is the sum from n=0 to infinity of 7/(3^n) ?

The sum from n=0 to infinity of 7/(3^n) is 21/2

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sum from n=0 to infinity of 7/(3^n)

n = 0 \sum \infty \frac{7}{3 ^{n}}

\frac{21}{2}

Decimal

10.5

Solution steps

n = 0 \sum \infty \frac{7}{3 ^{n}}

Apply the constant multiplication rule:

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

= 7 \cdot n = 0 \sum \infty \frac{1}{3 ^{n}}

Apply Series Geometric Test:

\frac{3}{2}

= 7 \cdot \frac{3}{2}

Simplify

7 \cdot \frac{3}{2} : \frac{21}{2}

= \frac{21}{2}

What is the sum from n=0 to infinity of 7/(3^n) ?
The sum from n=0 to infinity of 7/(3^n) is 21/2