问题标题:
已知数an=4n-1,bn=(1/n)(a1+a2+.+an).设bn的前n项和为sn,则lim(1/s1+1/s2+.+1/sn)=多少?
问题描述:
已知数an=4n-1,bn=(1/n)(a1+a2+.+an).设bn的前n项和为sn,则lim(1/s1+1/s2+.+1/sn)=多少?
李文锋回答:
a1+a2+...+an=-n+2n*(n+1)=2n^2+nbn=2n+1sn=n+n(n+1)=n^2+2n=n(n+2)1/sn=1/[n(n+2)]=0.5*(1/n-1/(n+2))极根=lim0.5*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+...+1/(n-1)-1/(n+1)+1/n-1/(n+2))=lim0.5*(1+1/2-1/(n+1)-1/(n...
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