For a positive integer n ,   1 + 1 x n is expanded in increasing powers of x . If three consecutive coefficients in this expansion are in the ratio, 2 :   5 :   12 , then n is equal to

Question

For a positive integer n , &#160; 1 + 1 x n is expanded in increasing powers of x . If three consecutive coefficients in this expansion are in the ratio, 2 : &#160; 5 : &#160; 12 , then n is equal to

Aicharya · Accepted Answer

C r - 1 n : C r n : C r + 1 n = 2 : 5 : 12 &#8658; C r n C r - 1 n = 5 2 and C r + 1 n C r n = 12 5 &#8658; n - r + 1 r = 5 2 and n - r r + 1 = 12 5 &#8658; 2 n - 7 r + 2 = 0 and 5 n - 17 r - 12 = 0 On solving n = 118 and r = 34

For a positive integer n ,   1 + 1 x n is expanded in increasing powers of x . If three consecutive…

Solution

For a positive integer n , &#160; 1 + 1 x n is expanded in increasing powers of x . If three consecutive…

Solution

For a positive integer n , 1 + 1 x n is expanded in increasing powers of x . If three consecutive…