Question

If (4ⁿ)/(n+1) < dfrac(2n)!(n!)², then P(n) is true for

• A. n≥ 1
• B. n>0
• C. n<0
• D. n≥ 2

Hint:

\binom2nn grows faster than (4ⁿ)/(n+1) for large n.

Answer 1

The Correct Option is D

((2n)!)/((n!)²)=\binom2nn is the central binomial coefficient. It is known that: \binom2nn > (4ⁿ)/(n+1) for n≥ 2 Hence, the given inequality holds for n≥ 2.