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Odd Sum (Posted on 2002-08-08) Difficulty: 2 of 5
Prove that the sum of consecutive odd numbers beginning at 1 (eg 1, 3, 5, ..) always adds up to a perfect square

See The Solution Submitted by Cheradenine    
Rating: 3.9000 (10 votes)

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Complete solution | Comment 15 of 17 |
Let S=1+3+5+.......to n terms.
Common difference =2,so the nth term=1+(n-1)*2=2n-1
S=1+3+5+......+(2n-5)+(2n-3)+(2n-1)
writing in reverse order
S=(2n-1)+(2n-3)+(2n-5)+.......5+3+1
Adding the two series
2S=2n+2n+2n+..........to n terms=2n.2
Therefore S=n^2


  Posted by danish ahmed khan on 2012-10-23 14:38:05
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