Tim finds a new way to write the nth term of an infinite geometric series
Tim worked on a few infinite series like with partial sums 1/3, 4/9, 13/27, 40/81, ' which goes to ' . Don asked Tim how to get from 81 to 40 in the 4th partial sum. His first discovery was that if you add the numerator and the denominator of the previous fraction you get 40. That was fine. Was there another way to generalize the nth partial sum? Tim came up with the following, which Don had never seen before:
which he generalized to
Fine job Tim!!
The limit of the right side above as n->∞, equals 1/2; done in Mathematica,
The nth partial sum starting with 2/5 (this took Don quite a while to figure out how to write this sum and then write it as aMathematica command):
To order Don's materials