数列1/2*5,1/5*2,1/8*1,...,1/(3n-1)(3n+2),...求它的前n项和

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数列1/2*5,1/5*2,1/8*1,...,1/(3n-1)(3n+2),...求它的前n项和

数列1/2*5,1/5*2,1/8*1,...,1/(3n-1)(3n+2),...求它的前n项和
数列1/2*5,1/5*2,1/8*1,...,1/(3n-1)(3n+2),...求它的前n项和

数列1/2*5,1/5*2,1/8*1,...,1/(3n-1)(3n+2),...求它的前n项和
1/(3n-1)(3n+2)=1/3*[1/(3n-1)-1/(3n+2)]
Σ1/(3n-1)(3n+2)=1/3*{[1/2-1/5]+[1/5-1/8]+...+[1/(3n-4)-1/(3n-1)]+[1/(3n-1)-1/(3n+2)]}
=1/3[1/2-1/(3n+2)]
=n/(6n+4)