00:01
Hi, from the question given that consider the given sequence sum of n is equal to 0 to n is equal to 0 to infinity n times of x plus 2 the whole power n divided by 3 to the power of n plus 1.
00:15
So, here we need to find the radius of convergence and the interval of convergence.
00:19
So, let a n is equal to n by 3 to the power of n plus 1 and a n plus 1 is equal to n plus 1 divided by 3 to the power of n plus 2.
00:31
So, limit n tends to infinity a n plus 1 divided by a n is equal to n plus 1 divided by 3 to the power of n plus 2 multiplied with 3 to the power of n plus 1 divided by n.
00:48
So, that is equal to limit n tends to infinity 1 by 3 times of 1 plus 1 by n.
00:58
Now, apply limit n tends to infinity.
01:00
So, we have 1 by 3.
01:02
Therefore, we conclude that the radius of convergence radius of convergence will be 1 divided by 1 by 3 which is equal to 3 interval of convergence...