Consider the following simple progression of whole and fractional numbers (with odd denominators):

1 1/3, 2 2/5, 3 3/7, 4 4/9, 5 5/11, 6 6/13, 7 7/15, 8 8/17, 9 9/19, …

Any term of this progression can produce a Pythagorean triplet, for instance:

4 4/9 = 40/9; the numbers 40 and 9 are the sides of a right triangle, and the hypotenuse is one greater than the largest side (40 + 1 = 41).

## Sum of Infinite Power Series

Have a look at the two distinct sums of series of powers below.

Same procedure, different result accuracy levels… Can you guess what went wrong in the operation of fig. 2?