`1)` -Đặt `A = 2 + 2^2 + 2^3 +........+ 2^100`
`A = ( 2 + 2^2 + 2^3 ) +.........+ ( 2^98 + 2^99 + 2^100 )`
`A = 2 . ( 1 + 2 + 4 ) +........+ 2^98 . ( 1 + 2 + 4 )`
`A = 2 . 7 +........+ 2^98 . 7`
`A = 7. ( 2 +.......+ 2^98 ) vdots 7`
→ `A : 7` dư `0`
`2) x + ( x + 1 ) + ( x + 2 ) +........+ ( x + 2004 ) + ( x + 2005 ) = 2005`
-Số số hạng là: `( 2005 - 0 ) : 1 = 1 = 2006` ( số hạng )
`x . 2006 + ( 2005 + 1 ) . 2006 : 2 = 2005`
`x . 2006 + 2006 . 1003 = 2005`
`x . 2006 + 2012018 = 2005`
`x . 2006 = 2005 - 2012018`
`x . 2006 = -2010013`
`x = -2010013 : 2006`
`x = (-2010013)/2006`