1/3+1/15+1/35+……1/4008003

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1/3+1/15+1/35+……1/4008003

1/3+1/15+1/35+……1/4008003
1/3+1/15+1/35+……1/4008003

1/3+1/15+1/35+……1/4008003
原式=1/2[1-1/3+1/3-1/5+1/5-1/7+…+1/2001-1/2003]
=1/2[1-1/2003]
=1001/2003

1/3+1/15+1/35+……1/4008003
=1/(1×3)+1/(3×5)+1/(5×7)+…………+1/(2001×2003)
=1/2×【2/(1×3)+2/(3×5)+2/(5×7)+…………+2/(2001×2003)】
=1/2×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+…………+1/2001-1/2003)
=1/2×(1-1/2003)
=1/2×2002/2003
=1001/2003