If the coefficients of r^ th ,(r+1)^ th and (r+2)^ th terms in the expansion of (1+x) n are in the ratio of 4: 15: 42 , then n-r=

Step-by-step solution

General term of (1+x)^ n is T _ r +1 = ^ n C _ r x^ r Coefficient of r^ th term = ^ n C _ r -1 Coefficient of (r+1)^ th term = ^ n C _ r Coefficient of (r+2)^ th term = ^ n C _ r +1 ^n C_ r-1 : ^n C_r: ^n C_ r+1 =4: 15: 42 ^n C _ r-1 ^n C _r = 4 15 19 r-4 n=4 ...(i) And, ^n C_r ^n C_ r+1 = 15 42 19 r-5 n=-14 ...(ii) Subtracting (ii) from (i) n=18 and r=4 n-r=14