Give example of a monotone subsequence of the sequence Sn=cos(n.π/3)

A monotone subsequence is a subsequence that is either increasing or decreasing, which we define as follows:

Here, we can create a subsequence by taking every sixth term:

• When n = 6,

• When n = 12, ,

and so on, and every such element will have a value of 1. This is a monotone subsequence.

so, converting firstly the mixed fractions to improper fractions and then "adding".