Question

Power Series: sigma n=1 n-> infinity ((n(n+1)^n)/4^n) so far ive gotten IxI < (1/4) how do i find the interval of convergence and radius of convergence?

Answer 1

you dont have x in your summation, how can you get |x| < 1/4?

Answer 2

woops sigma n=1 n-> infinity ((n(x+1)^n)/4^n) IxI < (1/4)

Answer 3

hello again btw :]

Answer 4

great :)

Answer 5

by using the root test, you will get the limit

(n^(1/n))[(x+1)/4]

Answer 6

since lim (n^(1/n)) = 1, for the series to converge, you get |x+1| < 4

Answer 7

oh okay hmm okay now how would I find the intervals of convergence?

Answer 8

the radius of convergence is 4, and it is around -1. So the interval we are interested is (-5,3)

Answer 9

okay so we plug in what makes it zero which in this case is -1, and how did you get the interval?

Answer 10

by solving |x+1| < 4.

-4 < x+1 < 4
-5 < x < 3

Answer 11

Ohhh! xD thanks

Answer 12

So check the convergence of the series at the end points

Answer 13

you're welcome

Answer 14

how would I know to apply the root test? ratio?