Mathematics

Problem

a, b, c

and

d

are any four consecutive coefficients in the expansion of

(1+x)^n

, then prove that: (i) \frac{a}{a+b} + \frac{c}{c+d} = \frac{2b}{b+c} (ii) \left( \frac{b}{b+c} \right)^2 > \frac{ac}{(a+b)(c+d)}, \text{ if } x > 0.