`a, S = 4^0 + 4^1 + .... + 4^19`
`⇒ 4S = 4^1 + 4^2 + ... + 4^20`
`⇒ 4S - S = (4^1 + 4^2 + ... + 4^20) - (4^0 + 4^1 + .... + 4^19)`
`⇒ 3S = 4^1 + 4^2 + ... + 4^20 - 4^0 - 4^1 - .... - 4^19`
`⇒ 3S = 4^20 - 4^0`
`⇒ 3S = 4^20 - 1`
`⇒ S = (4^20 - 1)/3`
`b,` Ta có: `S = 4^0 + 4^1 + .... + 4^19`
`⇒ S = (4^0 + 4^1) + ...... + (4^18 + 4^19)`
`⇒ S = 4^0 . (1 + 4) + ...... + 4^18 . (1 + 4)`
`⇒ S = 4^0 . 5 + ...... + 4^18 . 5`
`⇒ S = 5 . (4^0 + ...... + 4^18)` $\vdots$ `5`
`⇒ đpcm`
