anonymous 4 years ago What is the sum of the infinite series?

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

How do you get 4/625 on top?

6. anonymous

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

7. anonymous

Oh! The first term!

8. anonymous

Duh! Thanks!

9. anonymous

yw! :)