Given sn = 1 + q + q^2 +..........+ q^n and Sn = 1 + q+1/2 + (q+1/2)^2 + .... + (q+1/2)^n,

Question

Given s_n = 1 + q + q² +..........+ qⁿ and \(S_n = 1+ \frac{q+1}2 + \left(\frac{q+1}2\right)^2 + ....+\left(\frac{q+1}2\right)^n , q \ne 1\) then ⁿ⁺¹C₁ + ⁿ⁺¹C₂s₁ + ⁿ⁺¹C₃s₂ +.........+ ⁿ⁺¹C_n+1s_n =

(a) 2ⁿS_n

(b) S_n

(c) \(\frac{S_n}{2^n}\)

(d) None of these

Answer 1

Correct option is (a) 2ⁿS_n