[jyl]

It sort of looks like art and George used the same method? I like it, you see the pattern hidden in the progression.

I don't know if this teacher will like the "work backward" answer, she may prefer your method. She and I have had some email exchanges before on what is the "appropriate" solution to a homework problem.

Confession - I first tried the "write a single equation" approach. Took about 1 minute to decide that was going tp be too tedious. Then I drew a picture of a ruler being repeatedly bisected but the cuts being offset by 1, and started to vaguely grasp the pattern George showed. But fractions confuse me, and I also realized that any intuitive pattern would have to be laboriously proved (this teacher is big on "show your work"). George, in your solution, starting at "1st kid", I only had the patience for the next three lines - I'm lazy. So the idea of working backwards seemed easier, because I could simply type a formula into excel, copy the row seven times, and voilą.

Pretty sad, to pass up the elegant solution that reveals the hidden pattern, for the expedient one that lends itself to a spreadsheet.

Of course, if she gets the hint, my poor daughter will have to work it with a calculator.

This hotel is noisy. Hard to sleep.