1³+2³+3³+…+99³+100³ 2³+4³+6³+…+98³+100³
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 19:39:22
![1³+2³+3³+…+99³+100³ 2³+4³+6³+…+98³+100³](/uploads/image/z/7632116-44-6.jpg?t=1%26%23179%3B%2B2%26%23179%3B%2B3%26%23179%3B%2B%E2%80%A6%2B99%26%23179%3B%2B100%26%23179%3B+2%26%23179%3B%2B4%26%23179%3B%2B6%26%23179%3B%2B%E2%80%A6%EF%BC%8B98%26%23179%3B%EF%BC%8B100%26%23179%3B)
1³+2³+3³+…+99³+100³ 2³+4³+6³+…+98³+100³
1³+2³+3³+…+99³+100³ 2³+4³+6³+…+98³+100³
1³+2³+3³+…+99³+100³ 2³+4³+6³+…+98³+100³
根据(1+2+...+n)^2=1^3+2^3+...+n^3,1³+2³+3³+…+99³+100³=(1+2+...+100)^2=(100*101/2)^2=25502500.
2³+4³+6³+…+98³+100³=2^3*(1^3+2^3+...+50^3)=8*(1+2+...+50)^2=8*(50*51/2)^2=13005000.
1³+2³+3³+…+99³+100³ 2³+4³+6³+…+98³+100³
=100^2*101^2/4