(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)(2)1/(1乘_数学解答

(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000)
(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1)〕
(3)1/(1乘2乘3乘4)+1/(2乘3乘4乘5)+...+1/(17乘18乘19乘20)
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人气：187 ℃　时间：2020-04-13 08:56:37

解答

(1)1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.+1/(1+2+3+4+...+1000) =1+2(1/2-1/3+1/3-1/4+...+1/1000-1/1001)=1+2(1/2-1/1001)=2000/1001(2)1/(1乘4)+1/(4乘7)+...+1/〔(3N-2)乘(3N+1))=1/3(1-1/4+1/4-1/7+...+1/(3N-2)-1...