化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
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化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
化简:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)
=1/x-1/(x+4)
=4/x(x+4)
1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+1/[(x+3)(x+4)]+1/[(x+4)(x+5)]
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.....1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)
=1/(x+1)-1/(x+5)
=4/[(x+1)(x+5)]
这就是拆项法
1/x(x+1)=1/x+1/(x+1)
so原式=1/x-1/(x+4)=4/x(x+4)
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