Solution: 2015 Winter Midterm - 8
Author: Michiel SmidQuestion
What is the coefficient of $x^{17}$ in the expansion of $(17 + 2x)^{99}$?
(a)
$2^{82} \cdot 17^{17} \cdot {99 \choose 17}$
(b)
$2^{16} \cdot 17^{82} \cdot {99 \choose 16}$
(c)
$2^{17} \cdot 17^{82} \cdot {99 \choose 17}$
(d)
None of the above.
Solution
$=\sum^{99}_{k=0} \binom{99}{k}17^{99-k}{(2x)}^k$
$=\binom{99}{17}17^{82}{(2x)}^{17}$
$=\binom{99}{17}17^{82}2^{17}x^{17}$