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1/1X2+1/2X3+1/3X4+…… 1 / 2003 x2004 solved by item splitting method

1/1X2+1/2X3+1/3X4+…… 1 / 2003 x2004 solved by item splitting method

1/1X2+1/2X3+1/3X4+…… 1/2003X2004
=1-1/2+1/2-1/3+1/3-1/4+...+1/2003-1/2004
=1-1/2004
=2003/2004

3/(1x2)+3/(2x3)+3/(3x4)+.+3/(2003x2004)=?

Original formula = 3 (1 / 1 * 1 / 2 + 1 / 2 * 1 / 3 +...) +1/2003*1/2004)=3[(1/1-1/2)+(1/2-1/3)+…… +(1/2003-1/2004)]=2(1-1/2004)=6009/2004

(1/2006-1)(1/2005-1)(1/2004-1)...（1/1000-1)
Write out the process, explain! Urgent~~

=(-2005/2006)(-2004/2005)…… (-999/1000)
=-999/2006