+964 Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.
+1926 In order to solve this problem, we must find the common ratio of the numbers.
Since it's a geometric series, setting r as the common ratio, we get
\(r = .036 / .4 = 36 / 400 = 9 /100 = .09 \)
We can calculate the sum using a really handy formula.
\(\frac{a}{1-r}\) where a is the first number and r is the common ratio.
Plugging in the values we already now, we get that the sum is equal to
\( .4 / [ 1 -.09] = .4 / .91 = 40 /91 \)
So our final answer is 40/91
Thanks! :)
