1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)......+1/(2002*2005)+1/(2005*2008)

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1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)......+1/(2002*2005)+1/(2005*2008)1/(1*4)+1/(4*7)+1/(7*10)+1/(10*1

1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)......+1/(2002*2005)+1/(2005*2008)
1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)......+1/(2002*2005)+1/(2005*2008)

1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)......+1/(2002*2005)+1/(2005*2008)
1/[n×(n+3)]=[(1/n)-(1/n+3)]×1/3.按着这个式子,每一个都可以拆开,中间项全消了,只剩下1和1/2008.所以结果就是(1-1/2008)×1/3,也就是669/2008.希望楼主满意~~~

1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)......前n项和的公式
Sn=n/(3n+1)
当3n+1=2008时,n=669
1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)......+1/(2002*2005)+1/(2005*2008)=669/2008