1^2/1^3-(1^2+2^2)/(1^3+2^3)+.-(1^2+2^2+...+80^2)/(1^3+2^3+.+80^3)=?24*(1/2*3+1/4*5+.+1/20*21)-(1/1^2+1/(1^2+2^2)+.+1/(1^2+2^2+.+10^2))
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 02:12:52
![1^2/1^3-(1^2+2^2)/(1^3+2^3)+.-(1^2+2^2+...+80^2)/(1^3+2^3+.+80^3)=?24*(1/2*3+1/4*5+.+1/20*21)-(1/1^2+1/(1^2+2^2)+.+1/(1^2+2^2+.+10^2))](/uploads/image/z/10144560-48-0.jpg?t=1%5E2%2F1%5E3-%EF%BC%881%5E2%2B2%5E2%EF%BC%89%2F%EF%BC%881%5E3%2B2%5E3%EF%BC%89%2B.-%281%5E2%2B2%5E2%2B...%2B80%5E2%EF%BC%89%2F%EF%BC%881%5E3%2B2%5E3%2B.%2B80%5E3%EF%BC%89%3D%3F24%2A%281%2F2%2A3%2B1%2F4%2A5%2B.%2B1%2F20%2A21%29-%281%2F1%5E2%2B1%2F%281%5E2%2B2%5E2%29%2B.%2B1%2F%281%5E2%2B2%5E2%2B.%2B10%5E2%29%29)
1^2/1^3-(1^2+2^2)/(1^3+2^3)+.-(1^2+2^2+...+80^2)/(1^3+2^3+.+80^3)=?24*(1/2*3+1/4*5+.+1/20*21)-(1/1^2+1/(1^2+2^2)+.+1/(1^2+2^2+.+10^2))
1^2/1^3-(1^2+2^2)/(1^3+2^3)+.-(1^2+2^2+...+80^2)/(1^3+2^3+.+80^3)=?
24*(1/2*3+1/4*5+.+1/20*21)-(1/1^2+1/(1^2+2^2)+.+1/(1^2+2^2+.+10^2))
1^2/1^3-(1^2+2^2)/(1^3+2^3)+.-(1^2+2^2+...+80^2)/(1^3+2^3+.+80^3)=?24*(1/2*3+1/4*5+.+1/20*21)-(1/1^2+1/(1^2+2^2)+.+1/(1^2+2^2+.+10^2))
1^2+2^2+.n^2=n(n+1)(2n+1)/6
1^3+2^3)+.n^3=n^2*(n+1)^2/4
(1^2+2^2+.n^2)/(1^3+2^3)+.n^3)
=n(n+1)(2n+1)/6/n^2*(n+1)^2/4
=2(2n+1)/3n(n+1)
=2/3{1/n+1/(n+1)}
1^2/1^3-(1^2+2^2)/(1^3+2^3)+.-(1^2+2^2+...+80^2)/(1^3+2^3+.+80^3)
=2/3{1+1/2-1/2-1/3+1/3+1/4-1/4-1/5+.+1/78+1/79-1/79-1/80}
=2/3(1-1/80)
=2/3*79/80
=79/120
24*(1/2*3+1/4*5+.+1/20*21)-(1/1^2+1/(1^2+2^2)+.+1/(1^2+2^2+.+10^2))
=24*(1/2-1/3+1/4-1/5+.+1/20-1/21)-24(