Find the least value of n for which (^{3n}C_{2} > 0, n in R).
-
A.
(frac{1}{3}) -
B.
(frac{1}{6}) -
C.
(frac{2}{3}) -
D.
1
Correct Answer: Option C
Explanation
(^{3n}C_{2} > 0 implies frac{3n!}{(3n – 2)! 2!} > 0)
(frac{3n(3n – 1)(3n – 2)!}{(3n – 2)! 2} > 0)
(frac{3n(3n – 1)}{2} > 0)
(3n(3n – 1) > 0 implies n > 0; n > frac{1}{3})
The least number in the option that satisfies (n > 0; n > frac{1}{3} = frac{2}{3})