Katie found the partial sums to be: 1/2, 3/4, 7/8, 15/16, 31/32, 63/64, 127/128, ... We talked about what happens with these numbers. They get bigger, but never quite get to 1. Then she looked at the ones digits in the top and bottom of these fractions.
Katie said the
pattern 1/2, 3/4, 7/8, and 5/6 keeps repeating. I asked her why this happens...After a couple of days to think about this Katie said "All powers of 2 always end in 2, 4, 8, 6 in that order, and the top number is always 1 less than the bottom number". WELL DONE KATIE!! Now this is something Don had never seen before and that's what makes his teaching so exciting!