Consider a sequence of 101 term as `(.^(100)C_(0))/(1.2.3.4),(.^(100)C_(1))/(2.3.4.5),(.^(100)C_(2))/(3.4.5.6),.....(.^(100)C_(100))/(101.102.103.104)` If `n^(th)`​ term is greatest term of sequence, then n is equal to :- A)48 B)49 C)50 D)51

Options

A. 48
B. 49
C. 50
D. 51

Answer

B

Explanation

Let `T_(1+1)` is max.
`T_(1+1)=(.^(100)C_(r ))/((r+1)(r+2)(r+3)(r+4))`
`= (.^(104)C_(r+4))/(101.102.103.104)` is max, when
`r+4=52`
r = 48
so term is `49^(th)`