1-1/2+1/3-1/4+1/5-1/6+…+1/15=23*[1/( )+1/( )+1/( )+1/( )]

来源：百度知道编辑：UC知道时间：2024/09/20 10:38:23

1-1/2+1/3-1/4+1/5-1/6+…+1/15
＝1＋1/2+1/3＋1/4+1/5＋1/6+…+1/15－1-1/2-1/3-1/4-1/5-1/6-1/7
＝1/8＋1/9＋1/10＋1/11＋1/12＋1/13＋1/14＋1/15

8+15=23 9+14=23 ......

1/23×（1/8+1/15)＝1/120
1/23×（1/9+1/14)＝1/126
1/23×（1/10+1/13)＝1/130
1/23×（1/11+1/12)＝1/132
上式＝23×[1/(120)+1/(126)+1/(130)+1/(132)]

1-1/2+1/3-1/4+1/5-1/6+…+1/15=23*[1/(120 )+1/(126)+1/(130 )+1/(132 )]

(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