1*2+2*3+3*4+4*5+.+29*30
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/31 01:49:28
![1*2+2*3+3*4+4*5+.+29*30](/uploads/image/z/3921733-37-3.jpg?t=1%2A2%2B2%2A3%2B3%2A4%2B4%2A5%2B.%2B29%2A30)
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1*2+2*3+3*4+4*5+.+29*30
1*2+2*3+3*4+4*5+.+29*30
1*2+2*3+3*4+4*5+.+29*30
1+2+……+n=n(n+1)/2
1^2+2^2+……+n^2=n(n+1)(2n+1)/6
n(n+1)=n^2+n
所以1*2+2*3+……+n(n+1)=n(n+1)/2+n(n+1)(2n+1)/6
=n(n+1)[1/2+(2n+1)/6]
=n(n+1)(3+2n+1)/6
=n(n+1)(n+2)/3
所以1*2+2*3+3*4+4*5+.+29*30
此时n=29
=29*30*31/3
=(30-1)*(30+1)*30/3
=(30^2-1)*10
=(900-1)*10
=8990