SOLUTION: Prove that 2C(2n − 1,n) = C(2n,n) for all n

SOLUTION: Prove that 2C(2n − 1,n) = C(2n,n) for all n > 0

Question 1157253: Prove that 2C(2n − 1,n) = C(2n,n) for all n > 0
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

For computational purposes, C(a,b) can be viewed as a fraction with b terms in the numerator, starting with a and counting down, and with b terms in the denominator, starting with b and counting down.

In both these expressions, the denominator of the fraction is n! So to demonstrate that the two expressions are equivalent, we only need to show the the numerators are the same.

The numerator of the expression on the left is

2((2n-1)(2n-2)(2n-3)...(n+1)(n))

The numerator of the expression on the right is

(2n)(2n-1)(2n-2)(2n-3)...(n+1)

Clearly the two expressions are equivalent....

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