Question

If $\left|a\right|=\sqrt{3}\left|b\right|$, the greatest term in absolute value in the expansion of ${(a+b)}^{50}$ is

• A. $5$th
• B. $11$th
• C. $13$th
• D. $18$th

Answer 1

The correct option is D $18$th

$m=\left[\frac{(n+1)\left|b\right|}{\left|a\right|+\left|b\right|}\right]=\left[\frac{51}{\left|a\right|/\left|b\right|+1}\right]$
$=\left[\frac{51}{\sqrt{3}+1}\right]=\left[\frac{51(\sqrt{3}-1)}{2}\right]=18$
Thus the greatest term in absolute value is the 18th term