计算1/x(x+3)+1/(x+3)(x+6)+.+1/(x+27)(x+30)

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计算1/x(x+3)+1/(x+3)(x+6)+.+1/(x+27)(x+30)
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计算1/x(x+3)+1/(x+3)(x+6)+.+1/(x+27)(x+30)
计算1/x(x+3)+1/(x+3)(x+6)+.+1/(x+27)(x+30)

计算1/x(x+3)+1/(x+3)(x+6)+.+1/(x+27)(x+30)
1/x(x+3)==[1/x-1/(x+3)]/3
1/x(x+3)+1/(x+3)(x+6)+.+1/(x+27)(x+30)
=[1/x-1/(x+3)+1/(x+3)-1/(x+6)+---+1/(x+27)-1/(x+30)]/3
=[1/x-1/(x+30)]/3
=10/[x(x+30)]