請問找出最大的n值 使得1+2+3+…n 總和小於1000 該怎麼寫呢?
回答 (1)
2017-06-15 3:31 pm
Sol
n>0
1+2+3+…+n<1000
n(n+1)/2<1000
n(n+1)<2000
n^2+n<2000
n^2+2*(n/2)<2000
n^2+2*(n/2)+(1/2)^2<2000+0.25
(n+1/2)<2000.25
44^2=1936
45^2+2025
44.5^2=1980.25
So
n+1/2<45
n<44.5
n<=44
最大的n=44
n>0
1+2+3+…+n<1000
n(n+1)/2<1000
n(n+1)<2000
n^2+n<2000
n^2+2*(n/2)<2000
n^2+2*(n/2)+(1/2)^2<2000+0.25
(n+1/2)<2000.25
44^2=1936
45^2+2025
44.5^2=1980.25
So
n+1/2<45
n<44.5
n<=44
最大的n=44
收錄日期: 2021-04-30 22:17:31
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170615055433AAVcONT