December 21st, 2011, 06:24 AM  #1 
Newbie Joined: Dec 2011 Posts: 8 Thanks: 0  Define X
1/1 + 1/1+2 + 1/1+2+3 +...+ 1/1+2+3+...+X = 2012/2011 Sorry for the typing but I'm noob. 
December 21st, 2011, 07:47 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,417 Thanks: 1025  Re: Define X
Define x? x is the 24th letter of the alphabet; x is also used to indicate a wrong answer.

December 21st, 2011, 08:06 AM  #3 
Newbie Joined: Dec 2011 Posts: 8 Thanks: 0  Re: Define X
Sorry but the translation from my language came like this ... "X=?" Is that clear now ? 
December 21st, 2011, 08:11 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond  Re: Define X
1/1 + 1/(1 + 2) + 1/(1 + 2 + 3) + ... + 1/(1 + 2 + 3 + ... + X) = 2012/2011 implies 1/(1 + 2) + 1/(1 + 2 + 3) + ... + 1/(1 + 2 + 3 + ... + X) = 1/2011 but 1/(1 + 2) > 1/2011.

December 21st, 2011, 08:26 AM  #5 
Newbie Joined: Dec 2011 Posts: 8 Thanks: 0  Re: Define X
X can be below zero

December 21st, 2011, 08:30 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond  Re: Define X
Ok, what else about X? Real, rational, integer . . .?

December 21st, 2011, 08:32 AM  #7 
Newbie Joined: Dec 2011 Posts: 8 Thanks: 0  Re: Define X
X can be anything 
December 21st, 2011, 08:39 AM  #8 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond  Re: Define X
Is the series limited to a certain number of terms or a minimum/maximum number of terms?

December 21st, 2011, 08:51 AM  #9 
Newbie Joined: Dec 2011 Posts: 8 Thanks: 0  Re: Define X
No limits , no other terms.

December 21st, 2011, 09:07 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,642 Thanks: 2084 
The partial sums (from 1/1 onwards) can be given as 2/2, 4/3, 6/4, 8/5, 10/6, 12/7, etc. Notice the pattern? It doesn't reach 2012/2011.


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