00:01
Given the c on the form summation of the minus 1 power n times x power n divided by the root 3 of the n from 1 to infinity.
00:13
So we need to apply the ratio test here and then we will have the limit of the am plus 1 over a n and goes to infinity and because of the absolute value so we don't need to worry about the minus 1 power so, therefore we get the limit of end goes to infinity.
00:36
I am plus 1, so again the x power and plus 1 divided by the n plus 1 root 3.
00:45
And that's the i am just 1.
00:47
Now dividing by the n, so we need to multiply by the reciprocal.
00:50
So we'll be the root 3 of the n over the x bell n.
00:54
Now we see we can cancel the x bell and with this x bell on the top here.
01:00
And then we can also bring the x outside the limit.
01:03
Therefore, we have the absolute x outside times the limit of, we can put the big root 3 outside inside the n over m -dust 1, and just to infinity.
01:15
And the next time we can push the limit here inside the root 3.
01:20
Therefore we have absolute x times the root 3 of the limit of n over m does 1, and goes to infinity...