Find all series of consecutive positive integers whose sum is exactly 10,000.
__________________________________

What if we don't require the consecutive integers to (all) be positive?

First, we can see that some of the solutions require integral multiples of 10000. For example, 2000 divides 10000 5 times, so there are 5 terms: 2000, two above, and two below. Similarly, we can determine more sequences.

For negative terms, notice the symmetry about zero. Thus, for each positive term N starting a sequence, there is a sequence starting at (-(N-1)). The endpoints are the same. The sequences are:

{-9999,10000} to 10000

{-1997,1998} to 2002

{-387,388} to 412

{-296,297} to 328

{-17,18} to 142

 

 

 

 

Posted by Eric on 2004-07-21 09:34:05