0.9999.... = 1.0

[Jay520]

MDMAlliance said:

Oh, you were trying to say this?  That one seems to just be .9 + .09 + .009 repeating forever.  

However 9(1/10)/1-(1/10) = 1 

is not the same thing as .9 repeating.

Yeah it is. That's the formula for the sum of an infinite convergent geometric series...

a + ar + ar^2 + ar^3 + ar^4 ... repeating IS equal to a/(1-r)

That is the formula!

Now for a, input 9/10. And for r, input (1/10). This equals

9/10 + 9/10(1/10)^1 + 9/10(1/10)^2 + 9/10(1/10)^3 ....which equals .9 + .09 + .009  which equals 0.9999999

So 0.9999999 = 9/10 + 9/10(1/10) + 9/10(1/10)^2 + 9/10(1/10)^2 which equals, according to the official formula, 9/10 / [1-(1/10)]

which is 1.