How do you find the sum of the infinite geometric series 1 + 0.4 + 0.16 + 0.064 + . . .?

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Answer 1 · 2015-11-23T09:02:24

$5/3$

The terms you're summing are $a_n=(4/10)^n$ . In fact,

$a_0 = (4/10)^0 = 1$

$a_1 = (4/10)^1=4/10=0.4$

$a_2= (4/10)^2 = 16/100=0.16$ , and so on.

The general rule states that, if a series of the form

$sum_{n=0}^infty k^n$

converges, then in converges to $\frac{1}{1-k}$

Since in your case $k=4/10$ , the result is

$1/(1-4/10) = 1/(1-2/5) = 1/(3/5) = 5/3$