What is the sum from n=0 to infinity of (15)/(6^n) ?

The sum from n=0 to infinity of (15)/(6^n) is 18

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sum from n=0 to infinity of (15)/(6^n)

n = 0 \sum \infty \frac{15}{6 ^{n}}

18

Solution steps

n = 0 \sum \infty \frac{15}{6 ^{n}}

Apply the constant multiplication rule:

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

= 15 \cdot n = 0 \sum \infty \frac{1}{6 ^{n}}

Apply Series Geometric Test:

\frac{6}{5}

= 15 \cdot \frac{6}{5}

Simplify

15 \cdot \frac{6}{5} : 18

= 18

n = 0 \sum \infty \frac{3 n !}{n ^{2}}

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

n = 3 \sum \infty \frac{1}{( n ^{2} - 4 )}

n = 0 \sum \infty \frac{5 ^{n}}{n ^{2}}

n = 0 \sum \infty \frac{8}{( 1 - 7 n )}

What is the sum from n=0 to infinity of (15)/(6^n) ?
The sum from n=0 to infinity of (15)/(6^n) is 18