Calc II Power Series:
sum (0,∞) of (5x)^n
I'm told to use the ratio test to find the radius of convergence.
I get to
lim n-∞ of (5x)^(n+1)/(5x)^n = 5x (right?)
Now I'm confused where to go from here. Please correct me if the limit is wrong as well.

Thanks.

Question

Calc II Power Series:
sum (0,∞) of (5x)^n
I'm told to use the ratio test to find the radius of convergence.
I get to
lim n->∞ of (5x)^(n+1)/(5x)^n = 5x (right?)
Now I'm confused where to go from here. Please correct me if the limit is wrong as well.

Thanks.

turingtest · Answer

if the series converges then$$|5x|<1$$solve for x, that interval is the radius of convergence

anonymous · Answer

oh! okay that was way simpler than I was making it out to be. so I don't have to "plug in" infinity for n since there is no n, correct? 
so x<1/5 for the series to converge?

turingtest · Answer

it's an absolute value don't forget, so$$-\frac15<x<\frac15$$is the interval of convergence, and 1/5 is the radius of convergence

anonymous · Answer

okay great thanks! my professor doesn't place particular importance on absolute value for some reason but I will most definitely remember that for the future.