1/1x4+1/4x7+1/7x10+……+1/2005x2008佼佼我

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1/1x4+1/4x7+1/7x10+……+1/2005x2008佼佼我1/1x4+1/4x7+1/7x10+……+1/2005x2008佼佼我1/1x4+1/4x7+1/7x10+……+1/2005

1/1x4+1/4x7+1/7x10+……+1/2005x2008佼佼我
1/1x4+1/4x7+1/7x10+……+1/2005x2008
佼佼我

1/1x4+1/4x7+1/7x10+……+1/2005x2008佼佼我
1/1*4=1/3*(1/1-1/4)
1/4*7=1/3*(1/4-1/7)
依次可得:
原式=1/3*(1-1/4+1/4-1/7+1/7-1/10……+1/2002-1/2005+1/2005+1/2008)
=1/3*(1-1/2008)
=1/3*2007/2008
=669/2008

1/1x4=(1-1/4)/3
1/4x7=(1/4-1/7)/3
1/7x10=(1/7-1/10)/3
...
1/2005x2008=(1/2005-1/2008)/3
所以原式=(1-1/2008)/3=669/2008