I’m using the Twelve Days of Christmas (and perhaps a few extra days besides) to do something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on different techniques that I’ll use to try to convince students that .
Part 1: Converting the decimal expansion to a fraction, with algebra.
Part 2: Rewriting both sides of the equation .
Part 3: Converting the decimal expansion to a fraction, using infinite series.
Part 4: A proof by contradiction: what number can possibly be between and ?
Part 5: Same as Part 4, except by direct reasoning.