Consider the sequence ``('^(n)C_(0))/(1.2.3),("^(n)C_(1))/(2.3.4),('^(n)C_(2))/(3.4.5),....,` if `n=50` then greatest term is

Options

A. `30^(th)`
B. `24^(th)`
C. `26^(th)`
D. `27^(th)`

Answer

B

Explanation

`(b)` Let `T_(r+1) ge T_(r )`
`implies("^(n)C_(r ))/((r+1)(r+2)(r+3)) ge ('^(n)C_(r-1))/((r )(r+1)(r+2))`
`implies("^(n)C_(r ))/('^(n)C_(r-1)) ge (r+3)/(r )`
`implies(n-r+1)/(r ) ge (r+3)/(r )`
`impliesr le ((n-2)/(2))`
For `n=50impliesr ge 24`
So `24^(th)` and `25^(th)` terms of sequence are greatest.