00:01
To figure out where exactly this converges to and what interval so let's go ahead and take the root test since everything has a k power to it there as you can see here right to the k k even though this has to the k plus one that still counts so we're going to take the limit as an approach is infinity of the nth root of take the absolute value of so it's negative one to the end, 2 to the end, x at the end over 3 to the k plus 1, that could be 3 to the end, and then plus 1, b times 3.
00:40
So then we take that to account here.
00:43
So all of the ends go away here.
00:46
Abs value of negative 1 is 1, so then we just have 2x over 3.
00:51
Abs of the value thereof times, yes, because, so since this is the only one that doesn't have an nth root 2 of that here, then that would just go to that would be 3 to 1 over n, and the limit as n approaches infinity of that would equal to, it would make the exponent go to 0, which means that it would go to 1.
01:24
And so we have 2x over 3 less than 1 here, which means that the opposite value of x is less than 3 over 2.
01:33
So we get for negative 3 over 2, less than x, which is less than 3 over 2...