math help
2006-12-21 8:10 pm
1+2+3...+999,999,997+999,999,998+999,999,999+1,000,000,000+999,999,999+999,999,998+999,999,997+999,999,996......+3+2+1=?
回答 (2)
2006-12-21 8:30 pm
✔ 最佳答案
這類的速算是:如以1+2+...100, 有以下方法計算:
(1+100)*(100/2)=5050
如以1+2+...300, 有以下方法計算:
(1+300)*(300/2)=45,150
所以1+2+3....1,000,000,000, 計算是:
(1+1,000,000,000)*(1,000,000,000/2)=500,000,000,500,000,000
而999,999,999+...+3+2+1 =
500,000,000,500,000,000-1,000,000,000 = 499,999,999,500,000,000
兩個數加起便是答案
2006-12-22 1:35 am
1+2+3...+999,999,997+999,999,998+999,999,999+1,000,000,000+999,999,999+999,999,998+999,999,997+999,999,996......+3+2+1=?
=(1+999,999,999)999,999,999/2*2+1000000000
=1000000000*999999999+1000000000
=99999999900000000+1000000000
=100000000900000000
=(1+999,999,999)999,999,999/2*2+1000000000
=1000000000*999999999+1000000000
=99999999900000000+1000000000
=100000000900000000
收錄日期: 2021-04-12 23:52:42
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061221000051KK01081