Interesting solution. Mine based on yours... :-)

來源: 亂彈 於 2009-01-16 13:47:06 [] [博客] [舊帖] [給我悄悄話] 閱讀數 : (249 bytes)
回答: 每周一道奧賽題 (7) 由 本來清靜 於 2009-01-16 11:23:20

1) f(n) > (n/1+n/2+...+n/n)/n-1=1/2+1/3+...+1/n, so the limit of f(n) is +infinity

2) Let n+1 be a prime... f(n+1)=([(n+1)/1]+...+[(n+1)/n]+[(n+1)/(n+1)])/(n+1)=(1+[n/1]+[n/2]+...+[n/n]+1)/(n+1)=(2+nf(n))/(n+1) < f(n) when 2 < f(n).

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