00:01
This series and i want to find the radius and interval of convergence.
00:05
So if i have a series like this, the first thing i want to do, the first thing i want to think of is try the ratio test.
00:16
And so that'll be for our purposes, the limit as n goes to infinity of the absolute value of negative 1 to the n plus 1, x to the n plus 7 plus 1, so that's n plus 8 over n plus 1 plus 5, so that's n plus 6.
00:39
That's a sub n plus 1 and then we'll multiply by the reciprocal, so we'll have n plus 5 over negative 1 to the n, x to the n plus 7.
00:52
Let's clean this up a bit, we'll have the limit as n goes to infinity of, well the 1 to the n, negative 1 to the n cancels, x to the n plus 7 cancels, and so we'll be left with negative 1, x, and then ratio of n plus 5 over n plus 6.
01:16
This needs to be less than 1 to converge...