Question

Three consecutive binomial coefficient in the expansion of ${(1+x)}^n$ are in

• A. G.P.
• B. H.P.
• C. A.G.P.
• D. None of these

Answer 1

The correct option is D None of these

$(1+x{)}^n$
$=1+nx+\frac{n(n-1)x^2}{2!}...$
Considering $T_1,T_2$ and $T_3$
$\frac{n(n-1)}{2}.\left(1\right)$
$=\frac{n(n-1)}{2}$
$\ne n^2$
Hence they are not in G.P
$\frac{n(n-1)}{2}+\left(1\right)$
$=\frac{n^2-n+2}{2}$
$\ne 2n$
$\frac{2}{n(n-1)}+1$
$=\frac{n^2-n+2}{n^2-n}$
$\ne \frac{1}{n}$
Hence the answer is none of the above.