化简(x+1)(x+2)分之1+(x+2)(x+3)分之1+(x+3)(x+4)分之1+(x+4)(x+5)分之1的值
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(x+1)(x+2)分之1+(x+2)(x+3)分之1+(x+3)(x+4)分之1+(x+4)(x+5)分之1
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^2+6+5)
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^2+6+5)
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