$\frac{{{C_0}}}{1} + \frac{{{C_2}}}{3} + \frac{{{C_4}}}{5} + \frac{{{C_6}}}{7} + ....$=
$\frac{{{2^{n + 1}}}}{{n + 1}}$
$\frac{{{2^{n + 1}} - 1}}{{n + 1}}$
$\frac{{{2^n}}}{{n + 1}}$
None of these
Sum of odd terms is $A$ and sum of even terms is $B$ in the expansion ${(x + a)^n},$ then
If for positive integers $r> 1, n > 2$, the coefficients of the $(3r)^{th}$ and $(r + 2)^{th}$ powers of $x$ in the expansion of $( 1 + x)^{2n}$ are equal, then $n$ is equal to
$\sum\limits_{n = 0}^4 {{{\left( {1009 - 2n} \right)}^4}\left( \begin{gathered}
4 \hfill \\
n \hfill \\
\end{gathered} \right)} {\left( { - 1} \right)^n}$ is
The sum of last eigth coefficients in the expansion of $(1 + x)^{15}$ is :-
If the sum of the coefficients in the expansion of ${(1 - 3x + 10{x^2})^n}$ is $a$ and if the sum of the coefficients in the expansion of ${(1 + {x^2})^n}$ is $b$, then