A) n is any integer
B) n is an odd integer
C) n is an even integer
D) None of these
Correct Answer: B
Solution :
Let consecutive terms are \[^{n}{{C}_{r}}\]and \[^{n}{{C}_{r+1}}\] \[\Rightarrow \frac{n!}{(n-r)!r!}=\frac{n!}{(n-r-1)!(r+1)!}\] \[\Rightarrow \frac{1}{(n-r)(n-r-1)!r!}=\frac{1}{(n-r-1)!(r+1)r!}\] \[\Rightarrow r+1=n-r\,\Rightarrow n=2r+1\]. Hence n is odd.
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