The 13 th term in the expansion of (x²+ 2 x )^ n is independent of x , then the sum of the divisors of n is

Step-by-step solution

13th term in the expansion of (x²+ 2 x )^ n is given by aligned T ₁₃ &= ^ n C ₁₂ ( x ² )^ n -12 ( 2 x )¹² &= ^ n C ₁₂ x ^ 2 n -24 ( 2¹² x ¹² ) &= ^ n C ₁₂ x ^ 2 n -24-12 (2¹² ) &= ^ n C ₁₂ x ^ 2 n -36 (2¹² ) aligned If the 13 th term will be independent of x , then x ^ 2 n -36 must be 0 . i.e., 2 n -36=0 2 n =36 n =18 The divisors of n=18 are 1,2,3,6,9,18 and their sum =1+2+3+6+9+18=39