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

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

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

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

1.42857 \dots

Solution steps

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

Apply Series Geometric Test:

1.42857 \dots

= 1.42857 \dots

n = 1 \sum \infty (cos (2))^{n}

n = 2 \sum \infty ln (1)

n = 0 \sum \infty 2 n ln (1 + n)

n = 1 \sum \infty \frac{e ^{\frac{1}{n}} - 1}{n}

n = 1 \sum \infty 4 - 9 (0.6)^{n}

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