1/2+1/(2+4)+1/(2+4+6)+…1/（2+4+6+…200）

来源：百度知道编辑：UC知道时间：2024/06/07 06:32:16

1/2+1/(2+4)+1/(2+4+6)+…1/（2+4+6+…200）
=1/2+1/(2+4)+1/(2+4+6)+1/(2+4+6+8)+...+1/(2+4+6+8+...+200)
=1/2+1/6+1/12+1/20+…+1/(2+4+6+8+…+200)
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+…+1/(100*101)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…+1/100-1/101
=1-1/101
=100/101

An=2+4+6+。。。+2n=2*n*(n+1)/2=n(n+1)
1/An =1/n - 1/(n+1)
S=1-1/2+1/2-1/3+....=1- 1/101=100 /101

(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)× 1/2-1/2=? 1/1+1/2+1/3+1/4+。。。。+1/N 是多少 1/1+1/2+1/3+1/4+......1/2002＝？ 1-1/2+1/3-1/4+........1/99-1/100 3/2=2+1/1*2=1/1+1/2