Question

What is the sum of the infinite series?

Answer 1

\[\sum_{n=2}^{\infty} 2^n/3*5^{n+2}\]

Answer 2

I see that you can take out the 5^2 and multiply that with three then simplify to get \[(1/75)*(2/5)^n\]
which is a geometric series. But when I solve it out like you would a regular geometric series I get 1/45. But wolframalpha says 20

Answer 3

your idea is correct. lets make sure the arithmetic is correct

Answer 4

\[\frac{1}{75}\sum_{n=2}^{\infty}\left(\frac{2}{5}\right)^n=\frac{1}{75}\left(\frac{\frac{4}{625}}{1-\frac{2}{5}}\right)\]

Answer 5

How do you get 4/625 on top?

Answer 6

we are starting at n=2, not n=1. The first term of the sequence is 4/625.

Answer 7

Oh! The first term!

Answer 8

Duh! Thanks!

Answer 9

yw! :)