`A = 1 + $\frac{1}{5}$ + $\frac{1}{5^{2} }$ + $\frac{1}{5^{3} }$ + ... + $\frac{1}{5^{2021} }$`
`$\frac{1}{5}$.A = $\frac{1}{5}$ + $\frac{1}{5^{2} }$ + $\frac{1}{5^{3} }$ + ... + $\frac{1}{5^{2021} }$ + $\frac{1}{5^{2022} }$`
`→ A - $\frac{1}{5}$.A = 1 - $\frac{1}{5^{2022} }$`
`A.(1 - $\frac{1}{5}$) = 1 - $\frac{1}{5^{2022} }$`
` A.$\frac{4}{5}$ = 1 - $\frac{1}{5^{2022} }$`
`A = (1 - $\frac{1}{5^{2022} }$) : $\frac{4}{5}$ < $\frac{4}{5}$`
`Vậy A < $\frac{4}{5}$`
