Least positive integer just greater than $(1+0.00002{)}^{50000}$ is __________.

$(1+0.00002{)}^{50000}={\left(1+\frac{1}{50000}\right)}^{50000}$$=1+50000\times \frac{1}{50000}+{50000}_{{\mathrm{c}}_2}\frac{1}{{\left(50000\right)}^2}$+…….

$\frac{1}{{\left(50000\right)}^2}is very small so neglect higher powers$

Now we know that $2\le {\left(1+\frac{1}{\mathrm{n}}\right)}^{\mathrm{n}}<3\mathrm{\forall }\mathrm{n}\ge 1$

$\Rightarrow \text{ Least integer is }3$