If rth and (r + 1)th terms in the expansion of (p + q)^n are equal, then (n+1)q / r(p+q) is

Question

If rth and (r + 1)^th terms in the expansion of (p + q)ⁿ are equal, then \(\frac{(n+1)q}{r(p+q)}\) is

(a) 0 

(b) 1 

(c) \(\frac{1}{4}\)

(d) \(\frac{1}{2}\)

Answer 1

Answer : (b) 1

Given, (p + q)ⁿ 

∴ General term = T_{r + 1} = ⁿC_r p^{n – r} q^r 

∴  rth term = T_r = ⁿC_r–1 (p)^{n – (r – 1)} q^{r – 1} 

= ⁿC_{r – 1} p^{n – r + 1} q^{r – 1} 

(r + 1)th term = T_r+1 = ⁿC_r p^{n – r} q^r 

Given, T_r = T_{r + 1} 

⇒ ⁿC_{r – 1} p^{n – r + 1} q^{r – 1} = ⁿC_r p^{n – r} q^r