write the sequence of the squares of all
odd numbers. what is its algebra?
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OddSum = (Sum of Squares of all 2n numbers)
- (Sum of squares of first n even numbers)
= 2n*(2n+1)*(2*2n + 1)/6 - 2n(n+1)(2n+1)/3
= 2n(2n+1)/6 [4n+1 - 2(n+1)] = n(2n+1)/3 * (2n-1)
= n(2n+1)(2n-1)/3
Example:
Sum of squares of first 3 odd numbers = n(2n+1)(2n-1)/3 = 3(2*3+1)(2*3-1)/3 = 35 12 + 32 + 52 = 1 + 9 + 25 = 35
hope this will help u
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