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

1 Answer
Nov 23, 2015

#5/3#

Explanation:

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#