计算1/3*5+1/5*7+……+1/2001*2003

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计算1/3*5+1/5*7+……+1/2001*2003
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计算1/3*5+1/5*7+……+1/2001*2003
计算1/3*5+1/5*7+……+1/2001*2003

计算1/3*5+1/5*7+……+1/2001*2003
1/3*5+1/5*7+……+1/2001*2003
=1/2(1/3-1/5+1/5-1/7+……-1/2003)
=1/2(1/3-1/2003)
=1000/6009

1/3*5+1/5*7+……+1/2001*2003
=(1/2)*((1/3-1/5)+(1/5-1/7)......(1/2001-1/2003))
=(1/2)*(1/3-1/2003)
=500/2003

原式=1/2(1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9…………+ 1/2001 - 1/2003)
=1/2(1/3 - 1/2003)

1/3*5+1/5*7+……+1/2001*2003
=(1/2)*(1/3-1/5+1/5-1/7+……+1/1999-1/2001+1/2001-1/2003)
=(1/2)*(1/3-1/2003)
=(1/2)*(2000/6009)
=1000/6009

1000/6009