`A = (3 + 3² + 3³ + ...... +` $3^{2021}$) `.` `(3 . 31 - 279 . 3)`
Tách `3 + 3² + 3³ + ...... +` $3^{2021}$ ra ngoài biểu thức, đặt `3 + 3² + 3³ + ...... +` $3^{2021}$ `= B`
Ta có:
`B = 3 + 3² + 3³ + ...... +` $3^{2021}$
`3B = 3² + 3³ +` $3^{4}$ + ...... +` $3^{2021}$ `+` $3^{2022}$
`3B - B = 3² + 3³ +` $3^{4}$ + ...... +` $3^{2021}$ `+` $3^{2022}$ `- 3 - 3² - 3³ - ...... -` $3^{2021}$
`2B = $3^{2022}$ `- 3`
`B =` ($3^{2022}$ `- 3) : 2`
Khi đó:
A= ($3^{2022}$ `- 3)` `:` `2` `.` `3 . (31 - 279)`
= ($3^{2022}$ `- 3)` `:` `2 . (-744)`
= ($3^{2022}$ `- 3)` `:` `(-1488)`
