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Odd Sum (Posted on 2002-08-08)

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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Puzzle Solution: Method 2

| Comment 18 of 19 |

(In reply to Answer by K Sengupta)

We know that:

S(n) = (n/2)*{2a+(n-1)*d}, where:

S(n) = Sum of the given series to n terms

a = First term

d= common difference

In the given problem, we have:

a= 1 and, d=2, so that:

S(n)

= (n/2)*{2*1+(n-1)*2}}

= (n/2)*{2+2n-2}

= (n/2)*(2n)

= n^2

Consequently, the sum of the consecutive odd numbers beginning at 1 always adds up to perfect square.

Posted by K Sengupta on 2022-05-10 22:13:52

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