What is the sum from n=0 to infinity of 6(0.4)^n ?

The sum from n=0 to infinity of 6(0.4)^n is 10

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sum from n=0 to infinity of 6(0.4)^n

n = 0 \sum \infty 6 (0.4)^{n}

10

Solution steps

n = 0 \sum \infty 6 \cdot 0. 4^{n}

Apply the constant multiplication rule:

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

= 6 \cdot n = 0 \sum \infty 0. 4^{n}

Apply Series Geometric Test:

1.66666 \dots

= 6 \cdot 1.66666 \dots

Simplify

= 10

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What is the sum from n=0 to infinity of 6(0.4)^n ?
The sum from n=0 to infinity of 6(0.4)^n is 10