JEE Mains · Maths · STD 11 - 7. binomial theoram
The sum of the series
\(2 \times 1 \times{ }^{20} \mathrm{C}_4-3 \times 2 \times{ }^{20} \mathrm{C}_5+4 \times 3 \times{ }^{20} \mathrm{C}_6-5 \times 4\) \(\times { }^{20} \mathrm{C}_7+\ldots+18 \times 17 \times{ }^{20} \mathrm{C}_{20}\), is equal to
- A 30
- B 32
- C 34
- D 36
Answer & Solution
Correct Answer
(C) 34
Step-by-step Solution
Detailed explanation
\begin{aligned} & (1-\mathrm{x})^{20}={ }^{20} \mathrm{C}_0-{ }^{20} \mathrm{C}_1 \mathrm{x}+{ }^{20} \mathrm{C}_2 \mathrm{x}^2 \ldots . .+{ }^{20} \mathrm{C}_{20} \mathrm{x}^{20} \\ & \frac{(1-\mathrm{x})^{20}}{\mathrm{x}^2}=\frac{{ }^{20} \mathrm{C}_0}{\mathrm{x}^2}-\frac{{…
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