Question

if n is an Odd positive integer prove that coefficient of the middle terms in the expansion of (x+y)^n are equal​

Answer 1

Answer:

nC(n-1)/2 = nC(n+1)/2

Step-by-step explanation:

since n is odd, total terms are even & middle terms are two (n-1)/2 & (n+1)/2

now nC(n-1)/2 = n!/[n-(n-1)/2] [ (n-1)/2]!

= n!/[n+1/2]! [ (n-1)/2]!

again nC(n+1)/2 = n!/[n-(n+1)/2] [ (n+1)/2]!

n!/[n+1/2]! [ (n-1)/2]!

therefore, nC(n-1)/2 = nC(n+1)/2

hence the middle terms are equal