00:04
Now in this question, basically, we look at a few theories, and you asked whether the series have upper bond or lower bond, right? so, for example, in this first case a, and i suppose this has an upper bond, and that means as you increase n, then tn and t management should approach similar values, right? but you can see that this is impossible, because if you set the limit to be less the t, then these two sides will be the same, right? but this n we're going to infinite, right? so this can not be satisfied.
00:34
So this one does not really have an upper bond.
00:37
And in terms of the lower bond, the low bond, i think what we're talking about actually obviously is the same, but you cannot have a lower bond either.
00:45
I guess the lower bond means, and i suppose allen is always, you know, it's not active, right? so you can go from zero, one, something like that.
00:55
So basically this does not, this series does not have an up bond, right? nor does it have a low bond.
01:03
And why it, well, actually if, so this question we look at a view series, right? you ask you to find the upper bond, i mean if the upbound exists, right, of this series.
01:23
And if you look at the a and i could say that this series does not have upper bond, because if you suppose it has a hot point and then you know tn and tm and s1 must approach similar values, right? and if you said that to be the upper bond, and then this equation cannot be satisfied, right? so you cannot have upper bond here.
01:42
And, but if you look at the b, you can have out bond because as angle, it goes larger and larger, and this to approach upper bond, so they become the same, they become basically the same, right? and it's very clear that the upper bond of this tn, so that is tn going to infinite...