Question

In the binomial expansion of (a - b)ⁿ, n ≥ 5 the sum of the 5th and 6th terms is zero. Then, a/b equals

(a) (n - 5)/6

(b) (n - 4)/5

(c) 5/(n - 4)

(d) 6/(n - 5)

Answer 1

To find the value of a/b in the binomial expansion of (a - b)ⁿ, we can set the sum of the 5th and 6th terms equal to zero and solve for a/b. The correct answer is (a) (n - 5)/6.

Step-by-step explanation:

To find the sum of the 5th and 6th terms in the binomial expansion of (a - b)ⁿ, where n ≥ 5, we can use the binomial theorem.

The general term in the expansion is given by nCr * a^(n-r) * b^r, where r is the index of the term. So, the 5th term is nC4 * a^(n-4) * b^4 and the 6th term is nC5 * a^(n-5) * b^5.

Since the sum of the 5th and 6th terms is zero, we can set their sum equal to zero and solve for a/b. This gives us a/b = -n/(n-4).

So, the correct answer is (a) (n - 5)/6.