Proof of $(2n)!/(n!)^2\le2^{2n}$ by mathematical induction?
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How do I approach this problem using mathematical induction?
$$\frac{(2n)!}{(n!)^2} \leq 2^{2n}$$
binomial-coefficientsinduction
asked 2011-12-06
user id:20716
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You should verify it for $n=1$. Then show that when you assume it's true for $n=k$ it also holds for $n=k+1$. Or just realize the RHS is the sum of the binomial coefficients in the $2n$'th row of Pascal's triangle, and the LHS is one such element. – 2011-12-06