Prove that if and are positive integers and is a real number, then

Solution:

Step1

Given that

We have to prove that if m and n are positive integers and x is a real number, then

Step2

We have m and n are positive integers and x is a real number.

Suppose x= b+y where b is an integer and

Then we have

L.H.S(left hand side)

R.H.S(right hand side)

Here

Step3

Put value of x= b+y we get

Put value of x= b+y we get

As

Therefore, L.H.S=R.H.S