00:01
In this question, we are asked to find the interval of convergence for the given series.
00:05
And to do that, we will use the ratio test.
00:12
By the ratio test, we need to calculate the limit of the absolute value of a n plus 1 over a n, as n goes to infinity, where a n is the general term of the series.
00:32
To get a n plus 1, we simply need to replace n by n plus 1.
00:37
We'll get n plus 1 multiplied by x plus 6 to the n plus first power divided by 3 to the n plus first power.
00:49
And then we need to multiply that by the reciprocal of a n.
01:00
So this is what we'll get.
01:02
We need to take the limit as n goes to infinity.
01:05
We can cancel 3 to the n.
01:08
And n plus 1 factorial over n factorial becomes just n plus 1.
01:14
And we can also cancel x plus 6 to the n.
01:21
And we'll get the limit of the absolute value of n plus 1 divided by 3 multiplied by x plus 6...