First slide

Binomial theorem for positive integral Index

Question

The coefficient of x¹⁷ in the expansion of (x – 1) (x – 2) (x – 3) ... (x – 18) is

Moderate

A

$\frac{171}{2}$
B

342
C

– 171
D

684

Solution

Coefficient of x¹⁷ = – (1 + 2 + 3 + ... + 18)
$\begin{array}{l} = - \frac{18}{2} (1 + 18) \\ = - 9 \times 19 = - 171 \end{array}$

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