`b ) B = 3 + 3^2 + 3^3 + ... + 3^2021`

`=> 3B = 3^2 + 3^3 + 3^4 + ... + 3^2022`

`=> 3B - B = ( 3^2 + 3^3 + 3^4 + ... + 3^2022 ) - (3 + 3^2 + 3^3 + ... + 3^2021)`

`=> 2B = 3^2022 - 3`

`=> B = {3^2022 - 3}/2`

Vậy `B = {3^2022 - 3}/2`

`c ) C = 1 - 5 + 5^2 - 5^3 + ... - 5^2021 + 5^2022`

`=> C = 5^2022 - 5^2021 + 5^2020 - ... + 5 - 1`

`=> 5C = 5^2023 - 5^2022 + 5^2021 - ... + 5^2 - 5`

`=> 5C - C = (5^2023 - 5^2022 + 5^2021 - ... + 5^2 - 5 ) - ( 1 - 5 + 5^2 - 5^3 + ... - 5^2021 + 5^2022 )`

`=> 4C = 5^2023 - 1`

`=> C = {5^2023 - 1}/4`

Vậy `C = {5^2023 - 1}/4`

`d ) D = 7 - 7^2 + 7^3 - ... + 7^2013 - 7^2014`

`=> D = 7^2014 + 7^2013 - 7^2012 + ... - 7^2 + 7`

`=> 7D = 7^2015 + 7^2014 - 7^2013 + ... - 7^3 + 7^2`

`=> 7D - D = ( 7^2015 + 7^2014 - 7^2013 + ... - 7^3 + 7^2 ) - ( 7^2014 + 7^2013 - 7^2012 + ... - 7^2 + 7 )`

`=> 6D = 7^2015 - 7`

`=> D = {7^2015 - 7}/6`

Vậy `D = {7^2015 - 7}/6`

`#dtkc`

`b)B=3+3^2+3^3+...............+3^2021`
`3B=3^2+3^3+3^4+...................+3^2022`
`3B-B=(3^2+3^3+3^4+...................+3^2022)-(3+3^2+3^3+...............+3^2021)`
`2B=3^2022-3`
`B=(3^2022-3)/2`
Vậy `B=(3^2022-3)/2`
`c)C=1-5+5^2-5^3+.................-5^2021+5^2022`
`C=5^2022 - 5^2021 + 5^2020 -.................+ 5 - 1`
`5C=5^2023-5^2022+5^2021-..................+5^2-5`
`5C-C=(5^2023-5^2022+5^2021-..................+5^2-5)-(5^2022 - 5^2021 + 5^2020 -.................+ 5 - 1)`
`4C=5^2023-1`
`C=(5^2023-1)/4`
Vậy `C=(5^2023-1)/4`
`d)D=7-7^2+7^3-................+7^2013-7^2014`
`D=7^2014 + 7^2013 - 7^2012 +...............- 7^2 + 7`
`7D=7^2015+7^2014-7^2013+.................-7^3+7`
`7D-D=(7^2015+7^2014-7^2013+.................-7^3+7)-(7^2014 + 7^2013 - 7^2012 +...............- 7^2 + 7)`
`6D=7^2015-7`
`D=(7^2015-7)/6`
Vậy `D=(7^2015-7)/6`