Prove that if n is an odd integer, then ?n2/4? = (n2+ 3)/4.
Step 1 of 3
Solution:Step1Given thatWe have to prove that if n is an odd integer, then n2/4 = (n2+ 3)/4.Step2Given that n is an odd integer.Here,L.H.S(left hand side)=n2/4R.H.S(right hand side)=ThenSuppose n=2m+1 for some integer value of m.L.H.S=n2/4 Put value of n=2m+1 in n2/4 we get By using Since L.H.S= ----------(1)Step3From the value of n=2m+1n-1=2mPut value of m in equation (1) we get = = = = Therefore, L.H.S===R.H.SSo, if n is an odd integer, then n2/4 = (n2+ 3)/4 proved.
Textbook: Discrete Mathematics and Its Applications
Author: Kenneth Rosen
The full step-by-step solution to problem: 25E from chapter: 2.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. Since the solution to 25E from 2.SE chapter was answered, more than 298 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “Prove that if n is an odd integer, then ?n2/4? = (n2+ 3)/4.” is broken down into a number of easy to follow steps, and 13 words. This full solution covers the following key subjects: Integer, odd, prove. This expansive textbook survival guide covers 101 chapters, and 4221 solutions.