若S=18+198+1998+19998+199998+1999998+199……998（44个9）,则S的末四位数字的和是多少?_数学解答

若S=18+198+1998+19998+199998+1999998+199……998（44个9）,则S的末四位数字的和是多少?

人气：440 ℃　时间：2020-06-25 00:27:51

解答

S=18+198+1998+...+199...998
=(20-2)+(200-2)+(2000-2)+...+(2000...000-2)
=222...2220 -2×45 (其中,222...2220,共45个2)
=222...2220-90
2220-90=2130
2+1+3+0=6
后四位数字的和是6.