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

The sum from n=0 to infinity of 0.1^n is 1.11111…

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sum from n=0 to infinity of 0.1^n

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

1.11111 \dots

Solution steps

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

Apply Series Geometric Test:

1.11111 \dots

= 1.11111 \dots

\int \frac{1}{5 x + 6} d x

36 y^{^{''}} - y = x e^{\frac{x}{6}}

3 x + 8

\int \frac{3 x + 6}{( 2 x ^{2} + 8 x + 3 ) ^{2}} d x

y = \frac{8}{x - 2}, at x = 6

What is the sum from n=0 to infinity of 0.1^n ?
The sum from n=0 to infinity of 0.1^n is 1.11111…