1/2+1/6+1/12+1/20,...前30个数的和为多少.
来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 01:46:17
1/2+1/6+1/12+1/20,...前30个数的和为多少.
1/2+1/6+1/12+1/20,...前30个数的和为多少.
1/2+1/6+1/12+1/20,...前30个数的和为多少.
1/2+1/6+1/12+1/20+.前30个数的和
=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(30*31)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/30-1/31)
=1-1/31
=30/31
1/2+1/6+1/12+1/20,...
=1-1/2+(1/2-1/3)+(1/3-1/4)+…………+(1/29-1/30)+(1/30-1/31)
=1-1/31
=30/31
1/2+1/6+1/12+1/20+……+1/(30×31)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/30-1/31
=1-1/31
=30/31
1/2+1/6+1/12+1/20+...+ =1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+.....+1/30*31
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/30-1/31)
=1-1/31
=30/31
题目为:1/2+1/6+1/12+......
可以将分母拆分为:1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+......1/(30*31)
继续拆分1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+........+1/30-1/31
中间的都可以约去,,所以最后剩下1-1/31=30/31
还有问题可以继续提问数学有点差,请原谅...
全部展开
题目为:1/2+1/6+1/12+......
可以将分母拆分为:1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+......1/(30*31)
继续拆分1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+........+1/30-1/31
中间的都可以约去,,所以最后剩下1-1/31=30/31
还有问题可以继续提问
收起
原式=(1-1/2) + (1/2-1/3) + (1/3-1/4) ……=1-1/31=30/31