Starting at the origin O, a point W walks in either

positive or negative direction  with incrementing

absolute step sizes of 1,2,3,…, 2005. In other words,

the point W walks (+1 or –1 step )from the origin, then (+2 or –2 steps) from the last point,…,and finally (+2005 or –2005 steps) from the last point .

 

  Prove that the point W can not be at the origin

after finishing 2005 walks.

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


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