What is the sum from n=0 to infinity of 5*(2/3)^n ?

The sum from n=0 to infinity of 5*(2/3)^n is 15

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sum from n=0 to infinity of 5*(2/3)^n

n = 0 \sum \infty 5 \cdot (\frac{2}{3})^{n}

15

Solution steps

n = 0 \sum \infty 5 (\frac{2}{3})^{n}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty (\frac{2}{3})^{n}

Apply Series Geometric Test:

3

= 5 \cdot 3

Simplify

= 15

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

n = 600 \sum \infty \frac{1}{n}

n = 1 \sum \infty \frac{n}{e ^{7 n}}

n = 1 \sum \infty \frac{3 ^{n}}{6 ^{n}}

n = 1 \sum \infty 8 (0.1)^{n - 1}

What is the sum from n=0 to infinity of 5*(2/3)^n ?
The sum from n=0 to infinity of 5*(2/3)^n is 15