# E as an average

1. Mar 13, 2007

### Loren Booda

How can one generate the sequence of whole numbers x and y which converge upon the equality

(2x+3y)/(x+y) = e

?

2. Mar 14, 2007

### AKG

(2x+3y)/(x+y) = e gives x/y = (e-3)/(2-e), so it suffices to find a sequence of rationals which converges to (e-3)/(2-e). If the decimal expansion of (e-3)/(2-e) is given, then we can just set y = 1, 10, 100, 1000, 10000, ... and make the obvious choice for x.

3. Mar 14, 2007

### christianjb

Same as above- except use continued fractions for x/y=(e-3)/(2-e)