What is the sum from k=0 to infinity of (0.4)^k ?

The sum from k=0 to infinity of (0.4)^k is 1.66666…

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sum from k=0 to infinity of (0.4)^k

k = 0 \sum \infty (0.4)^{k}

1.66666 \dots

Solution steps

k = 0 \sum \infty 0. 4^{k}

Apply Series Geometric Test:

1.66666 \dots

= 1.66666 \dots

n = 1 \sum \infty n^{3} \frac{1}{n !}

n = 1 \sum \infty \frac{1}{( n - 1 ) !}

n = 2 \sum \infty \frac{9 n}{ln ( n )}

k = 1 \sum \infty [(\frac{k}{2 ^{k}})]

k = 0 \sum \infty - 1^{k}

What is the sum from k=0 to infinity of (0.4)^k ?
The sum from k=0 to infinity of (0.4)^k is 1.66666…