Q. 42 - Calculus

Question

Find the least upper bound of the sequences in Exercises 37–42 

$\{2,2.7,2.71,2.718,2.7182,\dots \}$

Step-by-Step Solution

Answer

The upper bound is $e.$

Step 1. Given information.

The given sequence is $\{2,2.7,2.71,2.718,2.7182,\dots \}.$

Step 2. Explanation.

The given sequence shows $2\le a_k<e\text{ for all }k\ge 1 \sin ce e\approx 2.718281828459045235360.$

The sequence possess least upper bound given by $e.$