Question Of The Day

The greatest term of (x + y)³⁰ when x = 11, and y = 4 is

a) 15^th

b) 16^th

c) 21^st

d) None of these

Ans: c) 21^st

The r^th term is given by. The ratio of the (r + 1)^th term to the r^th term is x(30 – r)/[y(r + 1)]. This ratio is initially mush greater than one (each term is much greater than the previous one), and then goes on reducing to less than 1. The r for which the ratio changes is the greatest term. For x = 11 and y = 4, the ratio becomes < 1 for r = 22, and the 21^st term is the greatest.