问题
选择题
(2-1)(2+1)(22+1)(24+1)(28+1)…(232+1)+1的个位数字为( )
A.2
B.4
C.6
D.8
答案
(2-1)(2+1)(22+1)(24+1)(28+1)…(232+1)+1
=(22-1)(22+1)(24+1)(28+1)…(232+1)+1
=(24-1)(24+1)(28+1)…(232+1)+1
=(28-1)(28+1)…(232+1)+1
=(216-1)…(232+1)+1
=264-1+1
=264;
∵21=2,22=4,23=8,24=16,个位数按照2,4,8,6依次循环,
而64=16×4,
故原式的个位数字为6.
故选C.