00:01
Okay, so what does it mean for a sum to converge? this means that, so let's look at the partial sum.
00:07
So look at sk, which is n equals 1 to k of a and plus bn, right? okay, but this is the same thing as the partial sum n equals 1 to k of a .n.
00:27
And then you have plus sum of n equals 1 to k of bn, right? so this is equal to the partial sum of a, let's say a, a n to the k, and then plus the partial sum of, the partial sum of bn up to k, right? okay, so what does it mean for to calculate what the limit is doing, what the series is doing, is we just have to look at limit as k goes to infinity of sk.
01:20
But note that this is the same thing as limit as k goes to infinity of skan plus skbn.
01:30
But we know that an converges.
01:33
So this converges to some s like a, let's say...