1x2+2x3+3x4+"""+99x100=1x(1+1)+2x(1+2)+â¦â¦99x(1+99)ï¼
=(1+2+3+â¦â¦+99)+(1^2+2^2+3^2+â¦â¦+99^2)ï¼
=4950+1/6 x 99x(99+1)x(2x99+1)ï¼
=4950+328350ï¼
=333300ãæ以åå¼=3x333300=999900.éç¨å
¬å¼ï¼1x2+2x3+3x4+â¦+n(n+1)=1x(1+1)+2x(2+1)+3x(3+1)+â¦n(n+1)=(1^2+2^2+3^2+â¦+n^2)+(1+2+3+â¦+n)=n(n+1)(2n+1)/6+n(n+1)/2=n(n+1)[(2n+1)+3]/6
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