00:01
Let's determine whether this sequence is increasing, decreasing, or perhaps not monotonic, then we'll determine whether it's bounded.
00:09
Now, let's go ahead and show that this sequence is decreasing.
00:14
So here, for any n bigger than or equal to 1, we'd like to show that a .n plus 1 is less than or equal to a .n.
00:26
Now this is equivalent to 1 over 2 n plus 1 plus 3, less than or equal to 1 over 2n plus 3.
00:39
And this is true since the denominator on the left hand side is smaller.
00:59
Excuse me, is larger.
01:01
Larger denominator means smaller fraction.
01:06
So by definition, an is decreasing.
01:16
That's what it means to be decreasing.
01:18
It means that the successor is no larger than the previous term.
01:24
Now let's go ahead and show that it's bounded...