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

\frac{d}{d x} (cos^{3} (x^{2} - x))

\int cos (m) y d y

n = 1 \sum \infty a^{n}

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} y + 4 x - 3 y + 2)

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…