回复：印度奥赛题（2星半）：无穷序列的最大值

Let S_k:=k^(1/k), then k=3 assumes the maximum value. Because S_k <= S_{k+1} yields k<=(1+1/k)^k which is monotone increasing from 2 to e=2.717828...
So k=2 is the last one that satisfies the inequality.