# Thread: Power Series Interval of Convergence

1. ## Power Series Interval of Convergence

hi
need help to see if i am doing this right.

i have the series

E (-1)^n+1 (x-1)^n / 5n

i have to find the interval of convergence for f(x), f'(x), F"(x), and the intergral of f.

i got the interval of convergence for f(x) but not sure its right. -9<x<11

for f'(x) i have

E (-1)^n+1 n(x-1)^n-1 / 5n

which equals (1/5)(x-1)<1
which equals -6<x<6

well im not sure im doing this right so yeah any help?

2. Originally Posted by Ricky007
hi
need help to see if i am doing this right.

i have the series

E (-1)^n+1 (x-1)^n / 5n

i have to find the interval of convergence for f(x), f'(x), F"(x), and the intergral of f.
Are we supposed to guess that f(x) is that sum?

i got the interval of convergence for f(x) but not sure its right. -9<x<11
That is not what I get. How did you get that?

for f'(x) i have

E (-1)^n+1 n(x-1)^n-1 / 5n

which equals (1/5)(x-1)<1
which equals -6<x<6
No, the sum is not equal to that! Perhaps you meant that the ratio test reduces to that- but that is not true either. How did you get (1/5)(x-1)< 1?

well im not sure im doing this right so yeah any help?
Pretty much nothing is correct here but since you don't show how you got these, I can't see how to correct it.

3. ## help

this is what i did. what did you get?

interval of convergence for f

E (-1)^n+1 (x-1)^n / 5n

lim (u_n+1 / u_n) = lim [(-1)^n+2 (x-1)^n+1 / 5n+10][5n / (-1)^n+1 (x-1)^n]

lim (-1)^n (x-1) / 10

(x-1) / 10 <1

-10<x-1<10
-9<x<11

im so lost here someone help!

4. Originally Posted by Ricky007
this is what i did. what did you get?

interval of convergence for f

E (-1)^n+1 (x-1)^n / 5n

lim (u_n+1 / u_n) = lim [(-1)^n+2 (x-1)^n+1 / 5n+10][5n / (-1)^n+1 (x-1)^n]
First, since the ratio test only applies to positive series, that should be absolute value of the ratio so the -1 disappears immediately. You should have $\displaystyle \frac{|x-1|^{n+1}}{5(n+1)}\frac{5n}{|x-1|^n= \frac{n+1}{n}|x-1|$. Now the only question is "What is the limit of $\displaystyle \frac{n+1}{n}$ as n goes to infinity?"

lim (-1)^n (x-1) / 10

(x-1) / 10 <1

-10<x-1<10
-9<x<11

im so lost here someone help!