00:01
Okay, to figure out the radius of convergence, you might, you know, just remember this shortcut here, that the radius of convergence is limit as n goes to infinity of absolute value of a .n over a .n plus 1, where the a .n is this chunk here, not including the x values.
00:24
If you don't remember that shortcut, then you can just use the ratio test on this whole chunk here and figure out when you're less than one.
00:33
Okay, but this is just a little shortcut so this is limit as n goes to infinity of absolute value of n squared over 2 times 4 times dot dot dot times 2n.
00:51
So that's just our a .n term.
00:54
And we're dividing by a n plus 1.
00:56
So multiplying by the reciprocal.
00:59
So 2 times 4 times dot dot dot times 2 n times 2 and plus 1.
01:14
And we're dividing by n plus 1 squared.
01:22
Okay, so this is limit as n goes to infinity.
01:28
N squared divided by n plus 1 squared.
01:30
That's the same thing as n divided by n plus 1 squared...