简算1/1*2+1/2*3+1/3*4+1/4*5+1/5*6......1/49*50
来源:百度知道 编辑:UC知道 时间:2024/07/02 12:01:11
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6......1/49*50=?
请问这种题有没有什么公式,这个是小学四年级的题,哎......
如果没有,那有啥子简便方法来算喃~
请问这种题有没有什么公式,这个是小学四年级的题,哎......
如果没有,那有啥子简便方法来算喃~
原式=1/2+(1/2-1/3)+(1/3-1/4)+........+(1/49-1/50)
=1/2+1/2+(-1/3+1/3)+(-1/4+1/4)+.....1/49-1/50
=1-1/50
=49/50
谢谢分给我 急用饿
用裂项级数的方法做:
1/1*2+1/2*3+1/3*4+...+1/49*50
=[1-1/2+1/2-1/3+1/3-1/4+...+1/49-1/50]
中间的都抵消,首尾各剩下一项
=1-1/50
=49/50
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6......1/49*50
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/49-1/50
=1-1/50
=49/50
1/2+1/(2*3)+1/(3*4)+...+1/[n*(n+1)]
=1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)
=1-1/(n+1)
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6......1/49*50=1-1/ (49+1)=49/50
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6......1/49*50=1-1/2+1/2-1/3+1/3-1/4.......+1/49-1/50
=1-1/50
=49/50
分解因为1/n*(n+1)=1/n-1/(n+1)所以1/1*2+1/2*3+1/3*4…1/49*50=1/1-1/2+1/2-1/3+1/3-1/4…+1/49-1/50=1-1/50=49/50(中间的全约了)
1/2-1/2=?
1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100)
1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100)
1+1/1+2+1/1+2+3+...+1/1+2+3...+2000
1+1/1+2+1/1+2+3.........+1/1+2+3.....100
1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=?
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
(1-1/2^2)*(1-1/3^2)*(1-1/4^2).......(1-1/100^2)
3/2=2+1/1*2=1/1+1/2
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)