Does 0.999... Equal 1?

[vlad321]

So here it goes, I hope this is not a joke thread because I'm about to waste 3 minutes of my life writing this up. From here on out S is sigma

0.999999 can be represented as the infinite sum of S(9 * (1/10) ^n) where n = 1 to infinity.This is basically sayying that 0.99999... = 9/10 +9/100 +9/1000 +....

Meanwhile the sum of a geometric series is PROVEN to be equal to :

a/(1-(1/r))

Where a is the first term, 0.9 in this case, and r is the rate of growth, 1/10 in this case. So where does that leave us?

0.9/(1-(1/10) =

= 0.9/( 9/10) =

= 0.9/0.9 =

= 1

 

 

And that is the easiest and way to prove this. The whole 0.3333 = 1/3rd is crap and not a real proof by any stretch of the imagination.