How does the minus come in Geometric Series I'm looking into the geometric series and can't understand how the 1 - .01 comes in below:
0.272727... = 0.27 + 0.0027 + 0.000027 + 0.00000027 + ...
             = 0.27 + 0.27(.01) + 0.27(.01)^2 + 0.27(.01)^3 + ...
             = 0.27 / (1-.01)
             = 0.27 / 0.99
             = 27/99
             = 3/11


Question is why do solve it using geometric progressions at all. When you use the basic method taught as kids in school, you're basically deriving the sum of an infinite GP unknowingly. Here's the easiest way-
x=0.272727272727...
And 100x=27.272727272727....
Thus, 99x=27
x=27/99
This is basically like deriving the sum of an infinite gp, only instead of a and r, we're using numbers here!
