计算1/1*2+1/2*3+1/3*4+…+1/2004*2005.

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计算1/1*2+1/2*3+1/3*4+…+1/2004*2005.
计算1/1*2+1/2*3+1/3*4+…+1/2004*2005.

计算1/1*2+1/2*3+1/3*4+…+1/2004*2005.
1/2+1/(2×3)+1/(3×4)……1/(2004×2005)
=1-1/2+1/2-1/3……+1/2004-1/2005
=1-1/2005
=2004/2005

1/1*2+1/2*3+1/3*4+…+1/2004*2005=1-1/2+1/2-1/3+1/3-1/4+…-1/2004+1/2004-1/2005=1-1/2005=2004/2005

1/2+1/(2×3)+1/(3×4)……1/(2004×2005)
=1-1/2+1/2-1/3……+1/2004-1/2005
=1-1/2005
=2004/2005