aqsafiaz08
aqsafiaz08 aqsafiaz08
  • 03-12-2019
  • Mathematics
contestada

n is a positive integer.Explain why n(n-1) must be an even number.
Please can someone explain this algebraically.

Respuesta :

KerryEye KerryEye
  • 09-12-2019

Answer:

n and (n - 1) are consecutive integers.

Step-by-step explanation:

We are given 'n', a positive integer.

This 'n' can either be odd or even.

Case I:

When 'n' is odd

The n - 1 is even.

Note that the product of odd and even is always even. That is the product of n and (n - 1) is even.

Case II:

when 'n' is even

Then n - 1 is odd.

Again, using the similar logic we can say that the product of n and n - 1 should be even because here, 'n - 1' is even and 'n' is odd.

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