A ratio of the 5 t h term from the beginning to the 5 t h term from the end in the binomial expansion of 2 1 3 + 1 2 3 1 3 10 is

Step-by-step solution

Total number of terms in the expansion of 2 1 3 + 1 2 3 1 3 10 = 10 + 1 = 11 Now, 5 t h term from end = 11 - 5 + 1 = 7 t h from beginning. We need to find a ratio of the 5 t h term from the beginning to the 5 t h term from the end (i.e. 7 t h term from beginning) in the binomial expansion of 2 1 3 + 1 2 3 1 3 10 = T 5 T 7 = 10 C 4 2 1 3 10 - 4 1 2 3 1 3 4 10 C 6 2 1 3 10 - 6 1 2 3 1 3 6     ∵ T r + 1 = n C r a n - r b r = 10 ! 4 ! 6 ! × 2 2 × 1 2 4 3 4 3 10 ! 6 ! 4 ! × 2 4 3 × 1