00:01
Let's use definition 2 to prove that this limit is 0, assuming the absolute value r is less than 1.
00:07
So first, case 1, r equals 0.
00:13
There's really nothing to show here.
00:16
The limit of rn is just the limit of 0 or the n equals 0.
00:22
If we really wanted to use the definition 2 for case 1, we can still use it.
00:29
Let epsilon be bigger than 0.
00:33
Then just let capital n be one.
00:39
If little n is bigger than capital n, then rn minus 0 is less than epsilon.
00:49
This is always true because since r equals 0, so rn minus 0 is just 0, and 0 is less than any positive number.
01:03
So that's the whole proof for case 1.
01:06
Now let's look at the more interesting case.
01:12
So we're still assuming that absolute value r is less than 1...