`@Kem`
Giải thích các bước giải:
`a, 19991999×1998-19981998×1999`
`=19991999×1998-19981998×1998-19981998`
`=(19991999-19981998)×1998 - 19981998`
`=10001×1998-1998×10001`
`=0`
`b,(2+4+6+...+100)×(36×333-108×111)`
`=(2+4+6+...+100)×(108×111-108×111)`
`=(2+4+6+...+100)×0`
`=0`
c, 2^100 - 2^99 - 2^98 - … - 2^2 - 2 - 1
`=2^100-(2^99+2^98+...+2^2+2+1)`
Đặt `S= 2^99+2^98+...+2^2+2+1`
`⇒2S =2(2^99+2^98+...+2^2+2+1)`
`⇒2S=2^100+2^99+...+2^3+2^2+2`
`⇒2S-S= (2^100+2^99+...+2^3+2^2+2)-(2^99+2^98+...+2^2+2+1)`
`⇒S=2^100-1`
`(1)`
`⇒ 2^100 - 2^99 - 2^98 - … - 2^2 - 2 - 1`
`=2^100-(2^99+2^98+...+2^2+2+1)`
`=2^100 - 2^100 - 1`
`=2^100-(2^100-1)`
`=2^100-2^100+1`
`=1`
