tính tổng a=7 mũ 2021-7 mũ 2019+...+ 7 mũ 5-7 mũ 3+7

Đáp án + Giải thích các bước giải:

`A = 7^2021 - 7^2019 + .... + 7^5 - 7^3 + 7`

`49A = 7^2023 - 7^2021 + .... + 7^7 - 7^5 + 7^3`

`49A + A = (7^2023 - 7^2021 + .... + 7^7 - 7^5 + 7^3 + 7) + (7^2021 - 7^2019 + .... + 7^5 - 7^3 + 7)`

`50A = 7^2023 - 7^2021 + .... + 7^7 - 7^5 + 7^3 + 7^2021 - 7^2019 + .... + 7^5 - 7^3 + 7`

`50A = 7^2023 + 7 + (-7^2021 + 7^2021) + (7^2019 - 7^2019) + ... + (7^3 - 7^3)`

`50A = 7^2023 + 7 + 0 + 0 + ... + 0`

`50A = 7^2023 + 7`

`A = (7^2023 + 7)/50`

Answer

`A = 7^{2021} - 7^{2019} + ... + 7^5 - 7^3 + 7`

`7^2A = 7^2 . (7^{2021} - 7^{2019} + ... + 7^5 - 7^3 + 7)`

`49A = 7^{2023} - 7^{2021} + ... + 7^7 - 7^5 + 7^3`

`49A + A = (7^{2023} - 7^{2021} + ... + 7^7 - 7^5 + 7^3) + (7^{2021} - 7^{2019} + ... + 7^5 - 7^3 + 7)`

`50A = 7^{2023} + 7`

`A = {7^{2023} + 7}/50`

Vậy `A = {7^{2023} + 7}/50`