Prove that if n is an integer, then [n/2]= n/2 if n is

Chapter 1, Problem 53E

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QUESTION:

Problem 53E

Prove that if n is an integer, then [n/2]= n/2 if n is even and (n – 1)/2 if n is odd.

Questions & Answers

QUESTION:

Problem 53E

Prove that if n is an integer, then [n/2]= n/2 if n is even and (n – 1)/2 if n is odd.

ANSWER:

Solution:

Step1

Given that

We have to prove that if n is an integer, then [n/2]= n/2 if n is even and (n – 1)/2 if n is odd.

Step2

When n is even.

Let n=2y

y=  ------(1)

For y as an integer.

Then put value of n we get

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