Review question

# If $x_1 = (x_0 + 2)/(x_0 + 1)$, can we show $\sqrt{2}$ lies between $x_0$ and $x_1$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8404

## Suggestion

…without using tables, show that each of $\dfrac{41}{29}$ and $\dfrac{99}{70}$ differ from $\sqrt{2}$ by less than $5 \times 10^{-4}$.

Without knowing $\sqrt{2}$, we can’t calculate the distance between $x_n$ and $\sqrt{2}$, but what’s the distance between $x_n$ and $x_{n+1}$?