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“The sum of the product of two successive even numbers and 1 is equal to the square of the odd number which is between the two even numbers.” Prove the above proposition. Proof Let n be an integer. We can say the two successive even numbers are 2 n and 2 n + 2 ; and the odd number which is between these even numbers is 2 n + 1 . If we make a sum of the product of these even numbers and 1, then we have : 2 2 n(2 n + 2 ) + 1 = 4 n 2 + 4 n + 1 = (2 n + 1 ) . Therefore, the sum is equal to the square of the odd number which is between the two even numbers.