Question

explain the answer for question

Answer 1

Given (a - b)^n can be written as a^n*(1 + (-b/a))^n.

a^n*(1 + (-b/a))^n = a^n{1 + n(-b/a) + n(n-1)(-b/a)^2/2 + n(n-1)(n-2)(-b /a)^3/3! + n(n-1)(n-2)(n-3)(-b /a)^4/4! + n(n-1)(n-2)(n-3)(n-4)(-b /a)^5/5! + ... }

Given that the sum of the 5th and 6th terms is zero.

n(n-1)(n-2)(n-3)(-b /a)^4/4! + n(n-1)(n-2)(n-3)(n-4)(-b /a)^5/5! = 0

On removing common factors, we get

(-b/a)^4/4! + (n-4)(-b/a)^5/5! = 0

1/4! + (n-4)(-b/a)/5! = 0

1 + (n-4)(-b/a)/5 = 0

5 = (n-4)(b/a)

a/b = (n-4)/5.

Hope this helps!