SOLUTION: Prove that nCr is less than or equal to n+1Cr+1
. Hint: Make use of the fact that if A ≤ B then A/B ≤1.
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Question 565266: Prove that nCr is less than or equal to n+1Cr+1
. Hint: Make use of the fact that if A ≤ B then A/B ≤1.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Pascal's triangle easily proves it, as
 = (n+1)C(r+1))
Since nC(r+1) is nonnegative, nCr <= (n+1)C(r+1).
Or, we can show that
C(r+1)} \le 1)
!r!}}{\frac{(n+1)!}{(n-r)!(r+1)!}} \le 1)
Multiply both numerator and denominator by 1/(denominator)
!}{(n+1)!r!} \le 1 \Rightarrow n!(r+1)! \le (n+1)!r!)
Divide both sides by n!r!
This is true because we're choosing r objects out of n, so it is reasonable to assume r <= n.
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