Answer
A sequence can be defined as a monotonic sequence that is either decreasing $(a_n=1, \dfrac{1}{2}, ....\dfrac{1}{2^n})$ or increasing $(a_n=1,2,...., n)$.
Work Step by Step
A sequence can be defined as a monotonic sequence that is either decreasing $(a_n=1, \dfrac{1}{2}, ....\dfrac{1}{2^n})$ or increasing $(a_n=1,2,...., n)$.
If a sequence is both monotonic and bounded, then it converges. A monotonic sequence of real numbers with $a_n \leq a_{n+1} $ for every $n \geq 1$ or $a_n \geq a_{n+1}$ for every $n \geq 1$, will consist of a finite limit $L$. This is possible only when the sequence is bounded.
