If n is an even natural number, then the product of its successor and predecessor is ___.

Given :

'n' is an even natural number.

To find :

We have to find the product of its successor and predecessor.

Solution :

n - even natural number.

Successor of $n  = n + 1$                  [odd natural number]

Predecessor of $n = n - 1$               [odd natural number]

Product of two odd natural numbers is an odd natural number.  

$(n + 1) (n - 1) = n^2 - 1^2 = n^2 - 1$         $[a^2 - b^2 = (a+b)(a-b)]$

Therefore, the product of n's successor and predecessor is $n^2 - 1$.

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Updated on: 10-Oct-2022

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