Question

The product of two consecutive natural numbers is​

Answer 1

Answer:

The product of two consecutive natural numbers is Even .

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Answer 2

Given, the two consecutive natural numbers are nn and (n+1)(n+1).

Now, the product of two consecutive natural numbers is n×(n+1)=n(n+1)n×(n+1)=n(n+1).

There are two possible cases:

Case 1: if a natural number nn is an even number.

Since nn is an even number, it can be written as 2m2m because every even number is divisible by 22.

So, the product of two consecutive natural numbers is 2m(2m+1)2m(2m+1).

Now, it is clearly visible that the product has 22 as one of the factors. So, the product is an even number.

Case 2: if a natural number nn is an odd number.

Since nn is an odd number, it can be written as 2m+12m+1 because every odd number is 11 more than its previous even number.

So, the product of two consecutive natural number is (2m+1)(2m+1+1)=(2m+1)(2m+2)(2m+1)(2m+1+1)=(2m+1)(2m+2).

Now, taking 22 as common. we get (2m+1)2(m+1)(2m+1)2(m+1)

Now, it is clearly visible that the product has 22 as one of the factors. So, the product is an even number.

Thus, the product of two consecutive natural numbers is always an even number.

Hope it helps you