00:01
We have to determine the series minus 1 power n, n scale, e power minus 2n is convergent or divergent.
00:13
We have to find it.
00:15
We will simply use the ratio test.
00:18
What the ratio test said? it said that if the limit of an plus 1 over an mod as n goes to infinity is less than 1, then our series is convergent.
00:33
Now, an is given here, negative 1 power n, n scale, e power negative 2n.
00:42
Just find this value.
00:43
It will be limit n approaches to infinity, minus 1 power n plus 1, n plus 1 whole scale.
00:54
I'm writing this as a denominator because it's a powerless negative, so it will be in the denominator.
00:59
Minus 2n plus 2.
01:03
An is minus 1 power n, n scale over e power minus 2n.
01:10
Just combine the terms here.
01:11
Minus 1 power n plus 1 and minus 1 power n.
01:15
Only minus 1 will be right here...