0.9999.... = 1.0

[MDMAlliance]

Jay520 said:

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. 

No, from my class, pretty much every time with these series it meant that these series APPROACHED these numbers.  However they never actually reached them.  In calculus you simplified them to such.  The formula is simply one that is used to handle more complex geometric series, such as ones that may approach a number like .253 or something.  

However, since the sum goes on infinitely, it does not ever actually equal to the number itself.