If a1, a2, a3 and a4 are the coefficient of any four consecutive terms in the expansion of (1 + ) |^n , prove that a1/a1+a2 + a3/a3+a4 = 2a2/ a2 + a3

Question

If a_1, a₂, a₃ and a₄ are the coefficient of any four consecutive terms in the expansion of (1 + )ⁿ , prove that \(\frac{a_1}{a_1+a_2}+\frac{a_3}{a_3+a_4}=\frac{2a_2}{a_2+a_3}\)

Answer 1

. Let a_{1 ,}a₂, a₃ and a₄ be the coefficient of four Consecutive terms T_{r + 1}, T_{r + 2}, T_{r + 3}, and T_{r + 4} respectively. Then 

a₁ = coefficient of Tr + 1 = ⁿC_r

a₂ = coefficient of T_r + 2 = ⁿC_{r + 1} 

a₃ = coefficient of T_r + 3 =ⁿC_{r + 2} and 

a₄ = coefficient of T_r + 4 = ⁿC_{r + 3}

Thus,