1/3+1/8+1/15+1/24+1/35+...+1/80+1/99 怎么解
来源:百度知道 编辑:UC知道 时间:2024/06/02 06:16:01
1/3+1/8+1/15+1/24+1/35+...+1/80+1/99
=1/2[(1-1/3)+(1/2-1/4)+...+(1/8-1/10)+(1/9-1/11)]
=1/2(1+1/2-1/10-1/11)
=36/55
一般项为1/[(n+1)^2-1]=1/n(n+2)=1/2[1/n-1/n+2]
1-1/3+1/2-1/4+1/3-1/5.。。。。1/98-1/100=3/2-1/99-1/100
1/3+1/8+1/15+1/24+1/35+...+1/80+1/99
=(1/2)*{[1-(1/3)]+[(1/2)-(1/4)]+[(1/3)-(1/5)]+...+[(1/7)-(1/9)]+[(1/8)-(1/10)]+[(1/9)-(1/11)]
=(1/2)*[1-(1/3)+(1/2)-(1/4)+(1/3)-(1/5)+...+(1/7)-(1/9)+(1/8)-(1/10)+(1/9)-(1/11)]
=(1/2)*[1+(1/2)-(1/10)-(1/11)]
=(1/2)*(72/55)
=36/55
1/3*5+1/5*8+1/8*11+......+1/98*101
1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+......+1/100 = ?
(1/2-1)*(1/3-1)*(1/4-1)*(1/5-1)*(1/6-1)*(1/7-1)*(1/8-1)*(1/9-1)*(1/10-1)
(1+1/3)*(1+1/8)*(1+1/15)*…*(1+1/99)
1/2,3/2,1/5,-1/8,-2/13,(?)
-1/2 1/2 -3/8 1/4 -5/32 ( )?
计算1+1/2+(1/3-1)+1/4+1/5+(1/6-1/2)+1/7+1/8+(1/9/1/3)......
3/1+8/7+3/2+1/8怎么算
1/2 1/3 2/5 3/8 5/13 ( )
3/2,2/3,3/4,1/3,3/8,( )