1/14+1/47+1/710+1/1013+.........+1/2002*2005

来源：百度知道编辑：UC知道时间：2024/06/30 05:06:08

简便方式~谢谢~！

1/1*4+1/4*7+1/7*10+1/10*13+.........+1/2002*2005
=[1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+.....+1/2002-1/2005]/3
=[1-1/2005]/3
=2004/(2005*3)
=668/2005

1/1*4=(1/1-1/4)1/3
1/4*7=(1/4-1/7)1/3
……
1/2002*2005=(1/2002-1/2005)1/3
1/1*4+1/4*7+1/7*10+1/10*13+……+1/2002*2005
=1/3(1/1-1/4+1/4-1/7+1/7-1/10+……+1/2002-1/2005)
=1/3(1-1/2005)
=1/3*2004/2005
=668/2005

1/1*4=(1/3)*(1-1/4);1/4*7=(1/3)*(1/4-1/7);………………
所以原式=(1/3)*(1-1/4+1/4-1/7+1/7-1/10+……+1/2002-1/2005)
=(1/3)*(1-1/2005)
=668/2005

通项式1/n(n+3)=1/3×[1/n-1/(n+3)]
所以原式=1/3×（1-1/4+1/4-1/7+1/7-1/10+...+1/2002-1/2005）
=1/3×（1-1/2005）=668/2005

(1+1/2+1/3+1/4)× (1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000) (1-1/4)(1-1/9)(1-1/16)^(1-1/4008004)(1-1/4012009) 1+1/2+1+1/3+1+1/4+......+1/100=? 1/1+1/2+1/3+1/4+。。。。+1/N 是多少 1-1/4 -1/8-1/16-1/32-1/64 1/1+1/2+1/3+1/4+......1/2002＝？ 1-1/2+1/3-1/4+........1/99-1/100 s=1/1+1/1!+1/2！+1/3！+1/4！+....+1/25! 1/2+1/4+1/8+1/16......+1/256=?