We observe that:

3.999....= 4 - x, where
x = (limit n -> infinity) (1/10^n)
= (limit m -> - infinity) (10^m), where m = -n
= 0

Consequently, 3.999... = 4 - 0 = 4

Edited on November 14, 2007, 2:12 pm

Posted by K Sengupta on 2007-11-14 03:57:50