Question

evaluate \[\sum_{n=1}^{\infty}{(2(0.1)^n+(0.2)^n)}\]

Answer 1

both geometric ..:

2 * (0.1)^n = 2 * (1/(1-(0.1))) = 2 2/9
(2/10)^n = (1/5)^n = 1/(1-(1/5)) = 1.25

add:

3 17/36

Answer 2

is it good ?

Answer 3

yes I got \[\frac{17}{36}\]as well