Question

Prove that the difference between any two corresponding terms of even natural numbers and odd natural numbers is 1

Answer 1

The difference between any two corresponding terms of even natural numbers and odd natural numbers is because -

First of all, we can write the generalised form of even and odd numbers in the following way-

• Even numbers - 2n, (here n= {0,1,2,3...} )

• Odd numbers - 2n+1, (here n= {0,1,2,3....} )

The difference between any corresponding even and odd number can be found using this generalised format.

=> (2n+1) - (2n)

=> 2n -2n + 1

=> 1

we can also check the above criteria by putting any value of n,

n= 1

=>3-2

=> 1

n=2

=>5-4

=>1

and so on hence the difference of corresponding even and odd terms will always be 1.

hence proved.