For x $ \in $ R, x $ \ne $ -1, if (1 + x)2016 + x(1 + x)2015 + x2(1 + x)2014 + . . . . + x2016 = $\sum\limits_{i = 0}^{2016} {{a_i}} \,{x^i},\,\,$ then a17 is equal to :

Question

For x $ \in $ R, x $ \ne $ -1,

if (1 + x)²⁰¹⁶ + x(1 + x)²⁰¹⁵ + x²(1 + x)²⁰¹⁴ + . . . . + x²⁰¹⁶ =

$\sum\limits_{i = 0}^{2016} {{a_i}} \,{x^i},\,\,$ then a₁₇ is equal to :

${{2017!} \over {17!\,\,\,2000!}}$

${{2016!} \over {17!\,\,\,1999!}}$

${{2017!} \over {2000!}}$

${{2016!} \over {16!}}$

Solution

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