1/1*2+1/2*3+1/3*4+1/4*5+.....+1/199*200要简便
来源:百度知道 编辑:UC知道 时间:2024/05/25 08:55:10
明天要用!急!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1/1*2+1/2*3+1/3*4+1/4*5+.....+1/199*200
=1-1/2+1/2-1/3+1/3-1/4+------+1/199-1/200
=1-1/200
=199/200
1/[n(n+1)]=1/n-1/(n+1)
原式=(1-1/2)+(1/2-1/3)+...+(1/199-1/200)
=1-1/200
=199/200
=(1-1/2)+(1/2-1/3)+(1/3-1/4)...(1/199-1/200)
=1-1/200
=199/200
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+....+(1/199-1/200)=1-1/2+1/2-1/3+1/3-.....-1/199+1/199-1/200=199/200
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/199-1/200)=1-1/200=199/200
1-1/2+1/2-1/3+1/3-1/4+.....+1/199-1/200=199/200
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
1+1/2+1/3+.....+1/n
1+1/2+1/3+...+1/100
1-1/2+1/3-.....-1/10
(1+1/2+1/3+1/4)×
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
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