WBJEE · Maths · Binomial Theorem
For \(x \in R, x \neq-1\), if \((1+x)^{2016}+x(1+x)^{2015}+x^{2}(1+x)^{2014}+\ldots \ldots .+x^{2016}=\sum_{i=0}^{2016} a_{i} \cdot x^{i}\), then \(a_{17}\) is equal to
- A \(\frac{2016 !}{17 ! 1999 !}\)
- B \(\frac{2016 !}{16 !}\)
- C \(\frac{2017 !}{2000 !}\)
- D \(\frac{2017 !}{17 ! 2000 !}\)
Answer & Solution
Correct Answer
(D) \(\frac{2017 !}{17 ! 2000 !}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} \mathrm{a}_{17} &=\text { coeffn of } \mathrm{x}^{17} \\ &={ }^{2016} \mathrm{C}_{17}+{ }^{2015} \mathrm{C}_{16}+{ }^{2014} \mathrm{C}_{15}+\cdots++{ }^{1999} \mathrm{C}_{0} \\ &={ }^{2016} \mathrm{C}_{1999}+{ }^{2015} \mathrm{C}_{1999}+{ }^{2014}…
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