Question

The sum of the coefficients of the first $10$ terms in the expansion of $(1-x{)}^{-3}$

• A. $220$
• B. $286$
• C. $120$
• D. $150$

Answer 1

The correct option is A $220$

For $(1-x{)}^{-3}$, the sum of the first r terms will be
${}^{n+r-1}{C}_n$
Replacing $n=3$ and $r=10$ in the above formula, we get
${}^{3+10-1}{C}_3$
$={}^{12}{C}_3$
$=\frac{\mathrm{12.11.10}}{3!}$
$=\frac{\mathrm{12.11.10}}{6}$
$=\mathrm{2.11.10}$
$=220$