求1/x(x+3)+1/(x+3)(x+6)+...+1/(x+15)(x+18)的值拜托各位了 3Q

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求1/x(x+3)+1/(x+3)(x+6)+...+1/(x+15)(x+18)的值拜托各位了 3Q

求1/x(x+3)+1/(x+3)(x+6)+...+1/(x+15)(x+18)的值拜托各位了 3Q
求1/x(x+3)+1/(x+3)(x+6)+...+1/(x+15)(x+18)的值拜托各位了 3Q

求1/x(x+3)+1/(x+3)(x+6)+...+1/(x+15)(x+18)的值拜托各位了 3Q
1/x(x+3) = 1/3 * ( 1/x - 1/(x+3) ) 1/(x+3)(x+6) = 1/3 * ( 1/(x+3) - 1/(x+6)) 1/(x+6)(x+9) = 1/3 * ( 1/(x+6) - 1/(x+9)) .相加后,得到:原式= 1/3 * (1/x - 1/(x+18)) = 17 / 3x(x+18)