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natulia [17]
3 years ago
14

Prove that the product of any two consecutive natural numbers is even.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
6 0

Answer with Step-by-step explanation:

Let us assume the 2 consecutive natural numbers are 'n' and 'n+1'

Thus the product of the 2 numbers is given by

Product=n(n+1)\\\\

We know that the sum of 'n' consecutive natural numbers starting from 1 is

S_n=\frac{n(n+1)}{2}\\\\\therefore n(n+1)=2\times S_n............(i)

Thus from equation 'i' we can write

Product=2\times S_n

As we know that any number multiplied by 2 is even thus we conclude that the product of 2 consecutive numbers is even.

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