1+1/3+1/6+1/10+...+1/5050

来源：百度知道编辑：UC知道时间：2024/05/31 16:18:58

越快越好，要有详细过程

裂项法
1+1/3+1/6+1/10+...+1/5050
=1+2/6+2/12+2/20+…+2/10100
=1+(2/2×3)+(2/3×4)+(2/4×5)+…+(2/100×101)
=1+2(1/2-1/3+1/3-1/4+1/4-1/5+…+1/100-1/101）
=1+2(1/2-1/101)
=200/101.

写通项。an=2/n(n+1)=2[1/n - 1/(n+1)]

1+1/3+1/6+1/10+...+1/5050
=2[1-1/2+1/2-1/3+…+1/100-1/101]
=200/101

(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) (1-1/100)(1-1/99)(1-1/98)......(1-1/3 1+1/2+1/3+.....+1/n 1+1/2+1/3+...+1/100 1+1/3+1/6+........+1/55 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) 3,1/3,1/3,1/,1/27,1/27( ) 1+1/2+1+1/3+1+1/4+......+1/100=?