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Consider the sequence ('^(n)C(0))/(1.2.3...

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

A

`30^(th)`

B

`24^(th)`

C

`26^(th)`

D

`27^(th)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(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.
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