UC知道1/6+1/12+1/20+1/30+···+1/（2005乘2006）
来源：百度知道 编辑：UC知道 时间：2024/05/31 20:33:29
简便运算
=(1/2 - 1/3)+(1/3 - 1/4)+....+ (1/2005 - 1/2006)
=1/2-1/2006
1/2*3=1/2-1/3
...
1/2005*2006=1/2005-1/2006
原式=1/2-1/3+1/3-1/4+...+1/2005-1/2006
=1/2-1/2006
=1002/2006
=501/1003
由裂项法
1/n(n+1)=(1/n)-[1/(n+1)]
所以原式=1-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/2005)-(1/2006)
=1-(1/2006)
=2005/2006
1/2+1/6+1/12+1/20+1/30
1/6+1/8+1/10+1/12+..........+1/202=?
-1/2-1/6-1/12-1/20-``````````````-1/4026042
1/2+1/6+1/12+......+1/1980+1/2070=?
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?
计算1/2 +1/6+1/12+1/20+1/30+1/42=
求解1/2-1/6-1/12-1/20-1/30-1/42
1/2+1/6+1/12+1/20+1/30......1/9900
1/3+1/6+1/12+1/24+1/48+…+1/1588