急求急求,这道题应该怎么做呢?有没有什么简便方法呢?
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1/(10*11)+1/(11*12)+....+1/(59*60)
=1/10-1/11+1/11-1/12+....+1/59-1/60
=1/10-1/60
=1/12
2/(10*9)+2/(9*8)+....+2/(5*4)+2/(4*3)
=2*【1/(10*9)+1/(9*8)+...+1/(5*4)+/(4*3)】
=2*(1/3-1/4+1/4-1/5+...+1/8-1/9+1/9-1/10)
=2*(1/3-1/10)
=2*7/30
=7/15
=1/10-1/11+1/11-1/12+....+1/59-1/60
=1/10-1/60
=1/12
2/(10*9)+2/(9*8)+....+2/(5*4)+2/(4*3)
=2*【1/(10*9)+1/(9*8)+...+1/(5*4)+/(4*3)】
=2*(1/3-1/4+1/4-1/5+...+1/8-1/9+1/9-1/10)
=2*(1/3-1/10)
=2*7/30
=7/15
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