Posted by Timofey on Friday, August 10, 2012 at 10:48am.
for k=1: 1 = 1(2-1)
assume for k
for n=k+1,
1+5+...+(4k-3)+(4(k+1)-3) = k(2k-1) + (4(k+1)-3)
= k(2k-1) + (4k+1)
= 2k^2 - k + 4k + 1
= 2k^2 + 3k + 1
= (k+1)(2k+1)
= (k+1)(2(k+1)-1)
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