Q. 14 - Calculus

Question

Give examples of sequences satisfying the given conditions or explain why such an example cannot exist.

An increasing sequence that is not strictly increasing.

Step-by-Step Solution

Answer

Examples of the sequences is $\left\{2,2,2,4,4,8,8,...\right\}$.

Step 1. Given information.

Consider the given question,

An increasing sequence that is not strictly increasing.

Step 2. Take the sequence a k .

Consider the sequence $\left\{a_k\right\}=\left\{2,2,2,4,4,8,8,...\right\}$.

The sequence is increasing sequence but is not strictly increasing sequence as $a_{k+1}\ge a_k$.

Hence, the sequence that is increasing sequence that is not strictly increasing in $\left\{a_k\right\}=\left\{2,2,2,4,4,8,8,...\right\}$.