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The number of positive integers satisfyi...

The number of positive integers satisfying the inequality `.^(n+1)C(n-2)-.^(n+1)C(n-1)<=100` is

A

9

B

8

C

5

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`.^(n+1)C_(n-2)-.^(n+1)C_(n-1) le 100`
`implies .^(n+1)C_(3)-.^(n+1)C_(2)le100`
`implies((n+1)n(n-1))/(6)-((n+1)n)/(2)le100` ,brgt `impliesn(n+1)(n-4)le600`
It is true for n=2,3,4,5,6,7,8,9.
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