What is the sum from n=0 to infinity of 7(0.1)^n ?

The sum from n=0 to infinity of 7(0.1)^n is 7.77777…

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sum from n=0 to infinity of 7(0.1)^n

n = 0 \sum \infty 7 (0.1)^{n}

7.77777 \dots

Solution steps

n = 0 \sum \infty 7 \cdot 0. 1^{n}

Apply the constant multiplication rule:

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

= 7 \cdot n = 0 \sum \infty 0. 1^{n}

Apply Series Geometric Test:

1.11111 \dots

= 7 \cdot 1.11111 \dots

Simplify

= 7.77777 \dots

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What is the sum from n=0 to infinity of 7(0.1)^n ?
The sum from n=0 to infinity of 7(0.1)^n is 7.77777…