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March 1, 2015

Posted by **Timofey** on Friday, August 10, 2012 at 10:48am.

1 + 5 + 9 + … + (4n -3)= n(2n-1)

- Calculus -
**Steve**, Friday, August 10, 2012 at 11:07amfor 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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