Odd addition
If the sum of the first odd numbers is of the form for positive integers and , find .
The answer is 110.
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1 solution
The sum of first n odd number is given by S n = k = 1 ∑ n ( 2 k − 1 ) = n ( n + 1 ) − n = n 2 . Therefore, for n = 1 0 1 0 1 0 0 , S n = ( 1 0 1 0 1 0 0 ) 2 = ( 1 0 2 ) 1 0 1 0 0 = 1 0 0 1 0 1 0 0 . Hence a + b = 1 0 0 + 1 0 = 1 1 0 .