A) \[\frac{(2n)\,!}{n\,!}\]
B) \[\frac{(2n)\,!}{{{2}^{n}}}\]
C) \[{{2}^{n-i}}\]
D) None of these
Correct Answer: A
Solution :
\[1\ .\ 3\ .\ 5......(2n-1)\,{{2}^{n}}\]\[=\frac{1\,.\,2\,.\,3\,.\,4.\,5.\,6....(2n-1)\,(2n)\,{{2}^{n}}}{2.\,4.\,6.....2n}\] \[=\frac{(2n)\,!\ {{2}^{n}}}{{{2}^{n}}(1\ .\ 2\ .\ 3......n)}=\frac{(2n)\ !}{n\ !}\].
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