1/(23)+1/(34)+1/(45)+.+1/(20082009)如何简算

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1/(2*3)+1/(3*4)+1/(4*5)+.+1/(2008*2009)如何简算
1/(2*3)+1/(3*4)+1/(4*5)+.+1/(2008*2009)如何简算

1/(2*3)+1/(3*4)+1/(4*5)+.+1/(2008*2009)如何简算
1/2-1/3+1/3-1/4+……+1/2008-1/2009
=1/2-1/2009
=2007/4018

1 2 3 4 1 2 3 4 1 2 3 4 1,2,3,4, 1 2 3 4 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1,2,3,4, 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1、2、3、4 1+2+3×4 1,2,3,4 1+2+3+4+.