An Equation With Squares

Let k ≥ 0, and let n = k(2k + 1). Then we have:

n2 + (n+1)2 + … + (n+k)2 = (n+k+1)2 + … + (n+2k)2.

For example,
02 = 0,
32 + 42 = 52,
102 + 112 + 122 = 132 + 142,
212 + 222 + 232 + 242 = 252 + 262 + 272,
and so on.

Leave a Reply

 

 

 

You can use these HTML tags

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>