Cho A = 4 + 4^2 + 4^3 + ... + 4^24 . CMR A chia hết 420

Ta có: A = 4 + $4^{2}$ `+` $4^{3}$ `+ ... +` $4^{24}$ 

`=> A = (4 +` $4^{2}$`) + (`$4^{3}$ `+` $4^{4}$`) + ... + (`$4^{23}$ `+` $4^{24}$`)`

`=> A = 1.(4 +` $4^{2}$`) +` $4^{2}$`.(4 +` $4^{2}$`) + ... +` $4^{22}$`.(4 +` $4^{2}$`)`

`=> A = 1.20 +` $4^{2}$`.20 + ... +` $4^{22}$`.20`

`=> A = (1 +` $4^{2}$ `+ ... +` $4^{22}$`).20`

`=> A` $\vdots$ `20`

Ta có: A = 4 + $4^{2}$ `+` $4^{3}$ `+ ... +` $4^{24}$ 

`=> A = (4 +` $4^{2}$ `+` $4^{3}$`) + ... + (`$4^{22}$ `+` $4^{23}$ `+` $4^{24}$`)`

`=> A = 4.(1 + 4 +` $4^{2}$`) + ... +` $4^{22}$`.(1 + 4 +` $4^{2}$`)`

`=> A = 4 . 21 + ... +` $4^{22}$ `. 21`

`=> A = (4 + ... +` $4^{22}$`).21`

`=> A` $\vdots$ `21`

Ta có: `A` $\vdots$ `20 ; 21`

`=> A` $\vdots$ `20 . 21`

`=> A` $\vdots$ `420 (dpcm)`

`#DungSenpai1412`