What is the sum from n=0 to infinity of 3/(8^n) ?

The sum from n=0 to infinity of 3/(8^n) is 24/7

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sum from n=0 to infinity of 3/(8^n)

n = 0 \sum \infty \frac{3}{8 ^{n}}

\frac{24}{7}

Solution steps

n = 0 \sum \infty \frac{3}{8 ^{n}}

Apply the constant multiplication rule:

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

= 3 \cdot n = 0 \sum \infty \frac{1}{8 ^{n}}

Apply Series Geometric Test:

\frac{8}{7}

= 3 \cdot \frac{8}{7}

Simplify

3 \cdot \frac{8}{7} : \frac{24}{7}

= \frac{24}{7}

n = 0 \sum \infty \frac{n ^{3}}{4 ^{n}}

n = 5 \sum \infty \frac{n + 1}{n ^{3}}

n = 0 \sum \infty \frac{1}{2 - n}

n = 0 \sum \infty (\frac{5}{7})^{n}

n = 1 \sum \infty \frac{n !}{9 ^{n}}

What is the sum from n=0 to infinity of 3/(8^n) ?
The sum from n=0 to infinity of 3/(8^n) is 24/7