What is the sum from n=0 to infinity of 4(3/5)^n ?

The sum from n=0 to infinity of 4(3/5)^n is 10

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sum from n=0 to infinity of 4(3/5)^n

n = 0 \sum \infty 4 (\frac{3}{5})^{n}

10

Solution steps

n = 0 \sum \infty 4 (\frac{3}{5})^{n}

Apply the constant multiplication rule:

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

= 4 \cdot n = 0 \sum \infty (\frac{3}{5})^{n}

Apply Series Geometric Test:

\frac{5}{2}

= 4 \cdot \frac{5}{2}

Simplify

4 \cdot \frac{5}{2} : 10

= 10

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What is the sum from n=0 to infinity of 4(3/5)^n ?
The sum from n=0 to infinity of 4(3/5)^n is 10