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化简1/(2*5)+1/(5*8)+1/(8*11)+…+1/[(3n-1)*(3n+2)]=
人气:175 ℃ 时间:2020-05-29 19:48:09
解答
1/[(3n-1)*(3n+2)]=1/3*{1/(3n-1)-1/(3n+2)}
原式=1/3*{1/2-1/5+1/5-1/8+1/8-1/11+...+1/(3n-1)-1/(3n+2)}
=1/3*{1/2-1/(3n+2)}
=n/(6n+4)
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