Prove that if n is an odd integer, then ?n2/4? = (n2+ 3)/4.

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.