Question

The power of ' $x$ ' which has the greatest coefficient in the expansion of ${\left(1+\frac{x}{2}\right)}^{10}$ is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (B)

$C_{r+1}={}^{10}{C}_r\frac{x^r}{2^r}$
For $r=2;{}^{10}{C}_2\frac{x^2}{2^2}\Rightarrow$ coefficient of $x^2=\frac{45}{4}=11\frac{1}{4}$
For $r=3;{}^{10}{C}_3\frac{x^3}{2^3}\Rightarrow$ coefficient of $x^3=15$
For $r=4;{}^{10}{C}_4\frac{x^4}{2^4}\Rightarrow$ coefficient of $x^4=\frac{210}{16}=\frac{105}{8}=13\frac{1}{8}\Rightarrow r=3\Rightarrow$ (B)