1/(1×2×3)+1/(2×3×4)+…+1/(100×101×102)

来源：百度知道编辑：UC知道时间：2024/06/28 17:09:21

用简便方法，急用！！！！！！！！！！！

1/(1×2×3)+1/(2×3×4)+…+1/(100×101×102)
=(1/2)×(1/1×2-1/2×3)+(1/2)×(1/2×3-1/3×4)+……+(1/2)×(1/100×101-1/101×102)
=(1/2)×[(1/1×2-1/2×3)+(1/2×3-1/3×4)+……+(1/100×101-1/101×102)]
=(1/2)×(1/1×2-1/101×102)
=(1/2)×(1/2-1/10302)
=2575/10302

利用公式：2/n(n+1)(n+2)=1/n(n+1)-1/(n+1)(n+2)
1/(1×2×3)+1/(2×3×4)+…+1/(100×101×102)
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+.....+1/100*101-1/101*102]
=1/2(1/2-1/10302)
=2575/10302

(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1) 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+1/2+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+1/1+2+1/1+2+3+...+1/1+2+3...+2000 1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=? (1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)