Series-5 (CAT-2006)

Consider a sequence where nth term, t_n = n/(n+2), n=1,2,...

The value of t₃*t₄*t₅*....*t₅₃ equals:

(1) 2/495        (2) 2/477        (3) 12/55        (4) 1/1485                       (5) 1/2970

Solution follows here:

Solution:

It’s a simple commonsense problem, involving no formulae.

t₃*t₄*t₅*....*t₅₃ = 3/5 * 4/6 * 5/7 * .......* 53/55

= 3*4*(5*6*7*....*53) / (5*6*7*...*53)*54*55

= 3*4 / 54*55 = 2/495

Answer(1)