求和Sn=1/(1*4)+1/(2*7)+.+1/n*(3n+1)
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求和Sn=1/(1*4)+1/(2*7)+.+1/n*(3n+1)
![求和Sn=1/(1*4)+1/(2*7)+.+1/n*(3n+1)](/uploads/image/z/16097768-8-8.jpg?t=%E6%B1%82%E5%92%8CSn%3D1%2F%281%2A4%29%2B1%2F%282%2A7%29%2B.%2B1%2Fn%2A%283n%2B1%29)
1/n(3n+1)=3[(3n+1-3n)/3n(3n+1)]=3[1/3n-1/(3n+1)]
Sn=3[(1/3+1/6+1/9+...+1/3n)-(1/4+1/7+1/10+...1/(3n+1))]
定义ψ(k)=lim[n→∞](lnn-(1/k+1/(k+1)+...+1/n))
则Sn=ψ(k+1)-ψ(k+4/3)+3-π√3/6-3ln3/2
Sn=3[(1/3+1/6+1/9+...+1/3n)-(1/4+1/7+1/10+...1/(3n+1))]
定义ψ(k)=lim[n→∞](lnn-(1/k+1/(k+1)+...+1/n))
则Sn=ψ(k+1)-ψ(k+4/3)+3-π√3/6-3ln3/2
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