Question

The constant term in expansion of (a/x^q + bx^p)ⁿ is____ th term

Answer 1

Correct option: (a) [(qn) / (p + q)] + 1

Explanation:

T_r+1 = ⁿc_r a^n–r b^r 

∴ T_r+1 = ⁿc_r (a / x^q)^n–r (bx^p)^r = ⁿc_r a^n–r b^r ∙ x^pr ∙ x^–qn+qr 

= ⁿc_r a^n–r b^r x^pr–qn+qr 

For constant term x^pr–qn+qr = x⁰ 

i.e.       pr + qr – qn = 0

∴ r = [(qn) / (p + q)] ⇒ r + 1 = [(qn) / (p + q)] + 1

∴ constant term is T_r+1 = T[1 + {(qn) / (p + q)}]

i.e. [{(qn) / (p + q)} + 1]^th term.