1/(1*3)+1/(3*5)+1/(5*7)+…+1/2007*2009等于几?

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1/(1*3)+1/(3*5)+1/(5*7)+…+1/2007*2009等于几?

1/(1*3)+1/(3*5)+1/(5*7)+…+1/2007*2009等于几?
1/(1*3)+1/(3*5)+1/(5*7)+…+1/2007*2009等于几?

1/(1*3)+1/(3*5)+1/(5*7)+…+1/2007*2009等于几?
(1/1×3)+(1/3×5)+(1/5×7)+…+(1/2007×2009)
=1/2*(1-1/3+1/3-1/5+...+1/2007-1/2009)
=1/2*(1-1/2009)
=1/2*2008/2009
=1004/2009