JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Analyzing +4 | -1

The coefficient of

x^{50}

in the binomial expansion of

\begin{array}{lr} (1+x)^{1000}+x(1+x)^{999}+x^{2}(1+x)^{998}+\ldots . \\ +x^{1000} \text { is: } \end{array}

View answer and explanation

Correct option: D

\frac{(1001) !}{(50) !(951) \text { ! }}

Option D (

\frac{{(1001) !}}{{(50) !(951) !}}

) is correct because by simplifying the given series and finding the coefficient of

x^{50}

in the resulting binomial expansion, we get

\frac{{(1001) !}}{{(50) !(951) !}}

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