The sum of the coefficients of three consecutive terms in the binomial expansion of 1 + x n + 2 , which are in the ratio 1 : 3 : 5 , is equal to

Step-by-step solution

Ratio of three consecutive terms in the binomial expansion of 1 + x n + 2 is C r - 1 n + 2 : C r n + 2 : C r + 1 n + 2 : : 1 : 3 : 5 So, ⇒ C r n + 2 C r - 1 n + 2 = 3 1 ⇒ n - r + 3 r = 3 ⇒ n + 3 = 4 r       . . . 1 And, C r + 1 n + 2 C r n + 2 = 5 3 ⇒ n + 2 - r r + 1 = 5 3 ⇒ 3 n + 6 - 3 r = 5 r + 5 ⇒ 3 n + 1 = 8 r       . . . 2 So, 3 4 r - 3 + 1 = 8 r ⇒ 12 r - 9 + 1 = 8 r ⇒ 4 r = 8 ⇒ r = 2 So, n = 5 Hence, we have 1 + x n + 2 = 1 +