Download “The sum of the product of two successive even numbers and 1 is

“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.