SOLUTION: the sum to infinity of 1/4 + 3/4² + 1/4³ + 3/4⁴ + ... is a. 1/5 b. 4/3 c. 7/3 d. 4/15 e. 7/15 thanks

Algebra ->  Finance -> SOLUTION: the sum to infinity of 1/4 + 3/4² + 1/4³ + 3/4⁴ + ... is a. 1/5 b. 4/3 c. 7/3 d. 4/15 e. 7/15 thanks       Log On


   

Question 1055762: the sum to infinity of 1/4 + 3/4² + 1/4³ + 3/4⁴ + ... is
a. 1/5 b. 4/3 c. 7/3 d. 4/15 e. 7/15
thanks
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
If you really want to solve this problem, then disintegrate this sequence in two geometric sequences

1%2F4 + 3%2F4%5E2 + 1%2F4%5E3 + 3%2F4%5E4+%2B+ellipsis+  =  (1%2F4 + 1%2F4%5E3+%2B+ellipsis+)  +  (3%2F4%5E2 + 3%2F4%5E4+%2B+ellipsis+%29)

and find the sum of each sequence separately.