Question

The values of the greatest term in $\sqrt{3}{\left(1+1/\sqrt{3}\right)}^{30}$ is

Answer 1

$\sqrt{3}\times {(1+\frac{1}{\sqrt{3}})}^{30}$

$\to \sqrt{3}\times [{}^{30}{c}_1{\left(\frac{1}{\sqrt{3}}\right)}^1+1{+}^{30}{c}_2{\left(\frac{1}{\sqrt{3}}\right)}^2{+}^{30}{c}_3{\left(\frac{1}{\sqrt{3}}\right)}^3+..{.}^{30}{c}_n{\left(\frac{1}{\sqrt{3}}\right)}^n+..{.}^{30}{c}_{30}{\left(\frac{1}{\sqrt{3}}\right)}^{30}]$

Value of greatest term ${\to }^{30}{c}_{15}\times {\left(\frac{1}{\sqrt{3}}\right)}^{15}\times \sqrt{3}$

$\to {}^{30}{c}_{15}\times \frac{1}{3^{15/2}}{3}^{1/2}$

$\to {}^{30}{c}_{15}\times \frac{1}{3^7}$