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
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
- [JEE MAIN 2016]
- A
$\frac{{2017\,!\,}}{{17\,!\,2000\,!}}$
- B
$\frac{{2016\,!\,}}{{17\,!\,1999\,!}}$
- C
$\frac{{2016\,!\,}}{{16\,!}}$
- D
$\frac{{2017\,!\,}}{{2000\,!}}$
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- [JEE MAIN 2020]