Definition:
A sequence (an) is set to be (i) monotonic increasing if an<=an+1(ii) Strictly monotonic increasing if an<an+1
(iii) Monotonic decreasing if an>=an+1
(iv) Strictly monotonic decreasing if an>an+1
A Sequence (an) is set to be monotonic if it is either monotonic increasing (or) decreasing.
Examples:
(i) 1,2,2,3,3,3,4,4,4,,4,...... is monotonically increasing sequence.
1<2, 3<=3
2<=2, 3<=3
2<3
(ii) 1,2,3,4,........ is a strictly monotonically increasing sequence.
(iii) 1,-1,1,-1,....... it is either monotonic increasing not decreasing.
(iv) A strictly monotonic decreasing equation in 1,1/2.1/3.1/4,.......
(v) (2 lower n-7)/(3 lower n+2) it is monotonic increasing sequence.
Note:
- A monotonic increasing sequence (an) is bounded below and a1 is the greatest lower bound of the sequence.
- A monotonic decreasing sequence (an) is the bounded above and a1 is the least upper bound of sequence.
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