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The number of positive integers satisfyi...

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

A

9

B

8

C

5

D

None of these

Text Solution

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To solve the inequality \( C(n+1, n-2) - C(n+1, n-1) \leq 100 \), we can start by rewriting the combinations in terms of factorials. ### Step 1: Rewrite the combinations Using the formula for combinations, we have: \[ C(n+1, n-2) = \frac{(n+1)!}{(n-2)!(3)!} = \frac{(n+1)n(n-1)}{6} \] \[ ...
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