Question

Use the Ratio Test to find the radius of convergence of SUM [x^n/2n^2 ]. So far I have...

Answer 1

take the limit of an/an-1

Answer 2

\[\lim \frac{x^n}{2n^2}\frac{2(n-1)^2}{x^{n-1}}\]

Answer 3

simplify and then take out all the notn parts

Answer 4

\[\lim x\frac{(n-1)^2}{n^2}\]

\[|x|\ \lim \frac{(n-1)^2}{n^2}\to\ |x|*1\]

|x|<1

you have a radius of 1

Answer 5

GREAT! I have that!!

Answer 6

.... if anything, you can always dbl chk with the wolf

Answer 7

http://www.wolframalpha.com/input/?i=SUM+%5Bx%5En%2F2n%5E2+%5D

Answer 8

haha, "the wolf"!!

Answer 9

Question: does it matter if |x|<1 or \[|x|\le 1\] ??

Answer 10

no, the radius is still 1

Answer 11

the interval of convergence is -1 to 1

Answer 12

Oooooh