UPDATE: all inlcuded in one PDF file if that is more convenient:

(see this post)______________________________________________________________

0.5

**5** ... = 5/9

How? The second 5 is repeating, so this is an infinite geometric series.

0.5

**5** ... = 0.5 + 0.05 + 0.005 + ...

first term is 1/2, and the ratio 0.05/0.5 = 5/50 = 1/10, so the sum of the terms of this infinite geometric

*progression* (sequence), called an infinite geometric series [the Sum, that is the series], would be (1/2)/(1-1/10) = (1/2)/(9/10) = (1/2)*(10/9) = 5/9

The notes included allow the spontaneous use of the vinculum over the repeating digits, but here on this board I would be forced to use bold or something to indicate such. I have to run. I hope the notes give you some insight into the numbers system's relation to infinite series ....

just a prelude to the Binomial Theorem notes. Maybe printing hard copy with hand-written notes, printed from device to actual hard copy print might trigger a sense of self-respect and dignity in yourself to validate your quest for understanding.

Prelude to Binomial Theorem ... 1 ...prelude page 2____________________________________________________________

TESTING 1, 2 ...

(will direct to another thread with door to jump into next post in this thread)