**Tara, a 6th grader, creates an infinite
series**

**Without any direction from
Don, Tara T created the following infinite series:**

**Tara had done 1/2 + 1/4 + 1/8 +...
before, as well as 1/3 + 1/9 + 1/27 +...The interesting thing she did was to
start with 1/4, then take 1/2 of each piece after that. And she realized that
the one she did above, was 1/2 less than 1, and would approach 1/2 !! This
couldn't be Don showed her, because she got
.516260... for the last partial sum, which is greater than 1/2. They talked
about this and she realized she had made a error getting the last denominator;
it should be 1/256. The partial sum came out to be 0.49609375... and she was
correct that the infinite series goes to 1/2!!!**

**Fine
work Tara!!**

**Tara had said that to get the top
number in the partial sum, just take 1/2 of the bottom, them subtract 1. Don
wrote this as**

**So
the sequence of partial sums goes to 1/2.**

Mathman home