00:01
In the given question, we need to show that if a1 is equal to 2, so we need to define the sequence as for a n plus 1 is equal to 1 upon 3 minus a .n.
00:14
So here if n is greater than 1, then it is bounded and decreasing the.
00:20
So here we have to state whether the sequence is convergent or divergent.
00:29
So now let's simplify our question.
00:34
So first of all, since it is given that a1 is equal to 2, we can show that a n plus 1 is less than or equal to a.
00:45
And we know that a .n is less than or equal to 2.
00:53
So here we will let as let y which is equal to a n plus 1 and x which is a .n.
01:04
So then our value for a n plus 1 will be equal to 1 upon 3 minus a and therefore y is equal to 1 upon 3 minus x.
01:19
So y upon x will be equal to 1 upon 3 by x minus 1 and if y minus x is negative then x is greater than 3 or we can say an is greater than 3.
01:42
So now we can use this induction to show that an is in between 0 to.
01:52
So here we will put as a1 is less than equal to 2...