What is the sum from n=0 to infinity of (0.3)^n ?

The sum from n=0 to infinity of (0.3)^n is 1.42857…

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sum from n=0 to infinity of (0.3)^n

n = 0 \sum \infty (0.3)^{n}

1.42857 \dots

Solution steps

n = 0 \sum \infty 0. 3^{n}

Apply Series Geometric Test:

1.42857 \dots

= 1.42857 \dots

n = 0 \sum \infty (1 + \frac{2}{5 n})^{n}

n = 1 \sum \infty \frac{n}{2 n ^{2} - 3}

n = 0 \sum \infty (\frac{7}{9})^{n}

n = 0 \sum \infty \frac{( n + 1 )}{n}

k = 1 \sum \infty k e^{- 6 k^{2}}

What is the sum from n=0 to infinity of (0.3)^n ?
The sum from n=0 to infinity of (0.3)^n is 1.42857…