For $x\, \in \,R\,,\,x\, \ne \, - 1,$ if ${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}} + ....{x^{2016}} = \sum\limits_{i = 0}^{2016} {{a_i\,}{\,x^i}} ,$ then $a_{17}$ is equal to
$\frac{{2017\,!\,}}{{17\,!\,2000\,!}}$
$\frac{{2016\,!\,}}{{17\,!\,1999\,!}}$
$\frac{{2016\,!\,}}{{16\,!}}$
$\frac{{2017\,!\,}}{{2000\,!}}$
If ${(1 + x)^n} = {C_0} + {C_1}x + {C_2}{x^2} + .......... + {C_n}{x^2},$ then $C_0^2 + C_1^2 + C_2^2 + C_3^2 + ...... + C_n^2$ =
The sum of the last eight coefficients in the expansion of ${(1 + x)^{15}}$ is
$\frac{{{C_0}}}{1} + \frac{{{C_2}}}{3} + \frac{{{C_4}}}{5} + \frac{{{C_6}}}{7} + ....$=
The sum of last eigth coefficients in the expansion of $(1 + x)^{15}$ is :-
If $(1 + x - 3x^2)^{2145} = a_0 + a_1x + a_2x^2 + .........$ then $a_0 - a_1 + a_2 - a_3 + ..... $ ends with