Question

The first three terms in the binomial expansion of (a+b)^n in ascending powers of b, are p,q and r respectively. show that q^2/pr = 2n/n-1

given that p=4, q=32, r=96. evaluate n

Answer 1

First 3 terms are a^2 + n a^(n-)1 b + n(n-1)/2 * a^(n-2) b^2

So q^2 / pr = (n^2 * a^(2n-2) * b^2 ) / (1/2 * a^n * (n(n-1) * a^(n-2) * b^2 )

= n^2 * a^2n-2 * b^2

-----------------------------------

1/2 n(n-1) * a^(2n-2) * b^2

= 2n / n - 1 as required

given p = 4, q=32 and r = 96:-

32^2 / 4*96 = 2n / n-1

2n / n-1 = 8/3

6n = 8n - 8

2n = 8

n = 4 answer