May 20th, 2013, 08:49 PM  #1 
Member Joined: Apr 2012 Posts: 64 Thanks: 3  find an item of series 
May 21st, 2013, 10:14 AM  #2 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: find an item of series
Every member of S is of the form , and S can be sorted in increasing order as follows: sort by greater z, then by greater y, and then by greater x. Let us consider the number of elements sorting by greater z: 1 element for z = 2 3 elements for z = 3... elements for z = k. Thus, up to z = k, there are a total of elements. The first k such that is 9, so for the 100th element, z = 9. Now the 120th element is , so we simply work backwards from there: The 113th element is The 112th element is The 106th element is The 105th element is The 100th element is . 

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