Ta có: A = 1 + 2 + 22 + 23 + ... + 22008 + 22009 + 22010
= 1 + 2 ( 1 + 2 + 22 ) + ... + 22008 ( 1 + 2 + 22 )
= 1 + 2 ( 1 + 2 + 4 ) + ... + 22008 ( 1 + 2 + 4 )
= 1 + 2 . 7 + ... + 22008 . 7 = 1 + 7 ( 2 + ... + 22008 )
Mà 7 ( 2 + ... + 22008 ) ⋮ 7. Do đó: A chia cho 7 dư 1.