# Series (Geometric?)

## Homework Statement

Calculate ##\sum\frac{4^{n+1}}{5^n}## (where n begins at 0 and approaches infinity).

## The Attempt at a Solution

I could easily solve this if the numerator were just ##4^n## instead of ##4^{n+1}##, because then it would be a geometric series with ratio of ##\frac{4}{5}##. But I'm not sure how to approach this one. Any help would be appreciated.

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UltrafastPED
Gold Member
What happens if you pull a 4 from every term - starting from n=1?

• 1 person
What happens if you pull a 4 from every term - starting from n=1?
Oh...so the problem becomes...
##4*\sum(\frac{4}{5})^n=4*\frac{1}{1-\frac{4}{5}}=4*5=20##
Is that right? Thanks!

Ray Vickson
Homework Helper
Dearly Missed
Oh...so the problem becomes...
##4*\sum(\frac{4}{5})^n=4*\frac{1}{1-\frac{4}{5}}=4*5=20##
Is that right? Thanks!
Well, do YOU think it is right?

Well, do YOU think it is right?
...yes? But then again, I wouldn't be here if I were always right just because I think I am.

Ray Vickson