0.9999.... = 1.0

[MDMAlliance]

Jay520 said:

MDMAlliance said:

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.  

You can calculate the sum of an infinite series. Not what it approaches, but what it equals. Not sure what else to tell you. You just can. 

http://en.wikipedia.org/wiki/Geometric_series

Look it up anywhere else and it will tell you the same.

In more formal language, a series converges if there exists a limit  such that for any arbitrarily small positive number , there is a large integer  such that for all ,
From wikipedia, http://en.wikipedia.org/wiki/Convergent_series

Note the whole "limit such that for any arbitrarily small positive number" refers to exactly what I'm talking about.