$\text{ Which term is numerically greatest in the expansion }(1+x{)}^{80}\text{ when }x=\frac{1}{3}$

$n=80;X=x=\frac{1}{3}$

$\text{ Now }\frac{(n+1)\left|X\right|}{\left|X\right|+1}=\frac{(80+1)\times \frac{1}{3}}{\frac{1}{3}+1}=\frac{81·\frac{1}{3}}{\frac{4}{3}}=20.2=20+0.2=p+F$

$\therefore \text{ Numerically greatest term is }{T}_{p+1}=T_{21}\left({21}^{\text{st }}\text{ term }\right)$