Q. 117 - Precalculus Enhanced with Graphing Utilities

Question

Use a calculator to compute the various values of the expression. Compare the values to e.

$2+\frac{1}{1+{\displaystyle \frac{1}{2+{\displaystyle \frac{2}{3+{\displaystyle \frac{3}{4+{\displaystyle \frac{4}{etc}}}}}}}}}$

Step-by-Step Solution

Answer

The table of the various values and the comparison to e is given below,

Step 1. Given information.

Consider the given question,

$2+\frac{1}{1+{\displaystyle \frac{1}{2+{\displaystyle \frac{2}{3+{\displaystyle \frac{3}{4+{\displaystyle \frac{4}{etc}}}}}}}}}$

Using a calculator, make a table of various values of the expression,

Step 2. Compare the values to e.

We know the value of e is $2.718281$.

Compare the result and the value of e,