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Hi, in this video we are going to discuss the convergence of divergence of this sequence, this is the sequence square root of n plus 1 minus square root of n.
00:15
As we see here, well, the first thing we are going to try to see is whether or not we can use algebra of limits.
00:22
But what we have here, this is the, our sequence is the difference of two other sequences.
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This sequence goes to infinity as n goes to infinity and this one goes to infinity as n goes to infinity.
00:36
That means both of these terms, this term and this term are sequences that diverts.
00:43
And that means we cannot apply algebra of limits.
00:47
Even if that doesn't ring a bell, just keep in mind that over here we have the expression infinity minus infinity, which is actually undefined.
01:00
So this expression over here is undefined.
01:03
We don't know what it is exactly.
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So we cannot use algebra of limits here.
01:09
That's it.
01:09
That's that.
01:10
So what we are going to do, since we cannot use algebra of limits, we can either use the definition of convergence or alternatively we can try to do some algebraic manipulations and bring this expression in a function...