The greatest coefficient (numerically) in ${\left(2\mathrm{x}-\frac{1}{3\mathrm{x}}\right)}^{10}$ is

${\left(2\mathrm{x}-\frac{1}{3\mathrm{x}}\right)}^{10}=(2\mathrm{x}{)}^{10}{\left(1-\frac{1}{6{\mathrm{x}}^2}\right)}^{10}\text{, }$

when $\mathrm{x}=1, \frac{(\mathrm{n}+1)\left|\mathrm{x}\right|}{\left|\mathrm{x}\right|+1}=\frac{11}{7}$; T₂ is N.G.T

$In {\left(2-\frac{1}{3}\right)}^{10},\left|T_2\right|={ }^{10}{C}_1{\left(2\right)}^9\left(\frac{1}{3}\right)=\frac{5120}{3}=1706.66$