If the coefficient of the middle term in the expansion of (1+x)2n+2 is α and the coefficients of middle terms in the expansion of (1+x)2n+1 are β and γ, then relation between α,β and γ is-
A
α+β+γ=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
α=β+γ
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
β=α+γ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
γ=β+α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Bα=β+γ (n+2)th term is the middle term in the expansion of (1+x)2n+2.
Therefore, α=2n+2Cn+1. (n+1)th and (n+2)th terms are middle terms in the expansion of (1+x)2n+1
Therefore, β=2n+1Cn and γ=2n+1Cn+1
Also, 2n+1Cn+2n+1Cn+1=2n+2Cn+1 (∵nCr+nCr+1=n+1Cr+1) ⇒β+γ=α