00:01
A simple test whether a certain series is divergent or not is to take the limit of your n -term of your series, and you take it to infinity.
00:18
And if the result is not zero, or if, say, the limit does not exist, then we can conclude that a -n is divergent.
00:34
In this case, we have a series defined by the first three terms.
00:38
Squared of one fourth, squared of two over six, squared of three over eight, and so on.
00:47
So here we can clearly see that the first three terms, the numerator of which is sum n, where your n is 1, 2, 3, and so on.
01:01
And then the denominator is sum 2n plus 2.
01:06
So to check, let's say a1 is the first term.
01:12
So we have that as 1 over 2 times 1 plus 2.
01:16
That gives us 1 4th.
01:19
And then here 8 .2 is 2 divided by 2 times 2 plus 2.
01:24
That's definitely 2 over 6...