Question

In the binomial (2^1/3 + 3^–1/3) ⁿ, if the ratio of the seventh term from the beginning of the expansion to the seventh term from its end is 1/6 then n =

• A. 6
• B. 9
• C. 12
• D. 15

Answer 1

Answer: (B)

9

Answer 2

T_{r + 1} = ⁿC_r a^n–r . b^r where a = 2^1/3 and b = 3^–1/3

T₇ from beginning = ⁿC₆ a^n–6 b⁶ and T₇ from end = ⁿC₆ b^n–6 a⁶ Ž $\frac{a^{n–12}}{b^{n–12}}$= $\frac{1}{6}$

Ž $2^{\frac{n–12}{3}}.3^{\frac{n–12}{3}}$ = 6^–1

Ž n – 12 = – 3

Ž n = 9