JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

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Analyzing +4 | -1

For

x \in {R}, x \neq-1

, if

(1+x)^{2016}+x(1+x)^{2015}+x^2(1+x)^{2014}+\ldots+x^{2016}=\sum\limits_{{i=0}}^{2016} a_i x^i,

then

a_{17}

is equal to:

View answer and explanation

Correct option: A

\frac{2017 !}{17 ! 2000 !}

Option A (

\frac{2017 !}{17 ! 2000 !}

) is correct because it represents the coefficient of

x^{17}

in the simplified expression after summing the geometric series.

More Questions from BINOMIAL THEOREM

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\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

\left( {n + 1} \right)

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

{x^5}

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n