计算3/1*4+3/4*7+3/7*10+...+3/(3n-5)(3n-2)+3/(3n-2)(3

发布时间：2021-03-16 10:44:12

计算3/1*4+3/4*7+3/7*10+...+3/(3n-5)(3n-2)+3/(3n-2)(3n+1)

网友回答

3/(3n-2)(3n+1)=1/(3n-2)-1/(3n+1)
原式=(1/1-1/4)+(1/4-1/7)+(1/7-1/10)+……+[1/(3n-2)-1/(3n+1)]
=1/1-1/4+1/4-1/7+1/7-1/10+……+1/(3n-2)-1/(3n+1)
=1-1/(3n+1)
=3n/(3n+1)
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