How Do I Ordinate?

Algebra Level 3

$\begin{matrix} A = \dfrac{2017+13}{2^{2017}+13}\\ \\ B = \dfrac{2017+14}{2^{2017}+14}\\ \\ C = \dfrac{2017+15}{2^{2017}+15} \end{matrix}$

A > B > C

A < B < C

A = B = C

1 solution

Tom Engelsman
Mar 27, 2018

We have a case of:

$A = \frac{x}{y}, B = \frac{x+1}{y+1}, C = \frac{x+2}{y+2}$

where $x < y$ . Taking the example $x = 1, y = 2$ , we obtain:

$\frac{1}{2} < \frac{2}{3} < \frac{3}{4}$

Hence by the same reasoning for $x = 2017 + 13, y = 2^{2017} + 13$ , we finally obtain $\boxed{A < B < C}.$