1x(1+2)/2+(1+2)X(1+2+3)/3+(1+2+3)X(1+2+3+4)/4+.+(1+2+3+.+99)X(1+2++3+...99+100)/100

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/16 19:56:52
1x(1+2)/2+(1+2)X(1+2+3)/3+(1+2+3)X(1+2+3+4)/4+.+(1+2+3+.+99)X(1+2++3+...99+100)/1001x(1+2)/2+(1+2)X(

1x(1+2)/2+(1+2)X(1+2+3)/3+(1+2+3)X(1+2+3+4)/4+.+(1+2+3+.+99)X(1+2++3+...99+100)/100
1x(1+2)/2+(1+2)X(1+2+3)/3+(1+2+3)X(1+2+3+4)/4+.+(1+2+3+.+99)X(1+2++3+...99+100)/100

1x(1+2)/2+(1+2)X(1+2+3)/3+(1+2+3)X(1+2+3+4)/4+.+(1+2+3+.+99)X(1+2++3+...99+100)/100
an的通项公式是
an=[n(n+1)/2*(n+1)(n+2)/2]/(n+1)=1/4n(n+1)(n+2)=1/4(n^3+3n^2+2n)
Sn=1/4[1/4n^2(n+1)^2+3*1/6n*(n+1)(2n+1)+2*n*(n+1)/2]
=1/4[1/4n^2(n+1)^2+1/2n*(n+1)(2n+1)+n*(n+1)]
不化简了
原式=S99=1/4[1/4*99^2*100^2+1/2*99*100*199+99*100]=6374362.5

第n项是(1+2+.....+n)*(1+2+......+(n+1))/(n+1)=(1+n)*n/2*(1+n+1)*(n+1)/2/(n+1)

找规律

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