請問除了MI之外，還有沒有其他方法能證明此不等式？
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證不等式1+...+1/(n^k-1)>n/2
2011-11-18 12:18 pm
回答 (2)
2011-11-18 5:30 pm
✔ 最佳答案
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2011-11-18 09:31:20 補充：
Grateful thanks should be given to bean_bottom_2 for his/her opinion
參考: 原創答案 + opinion
2011-11-18 5:05 pm
Let S be the series
S - 1 + 1/(2^n) = 1/2 + 1/3 + 1/4 ... + 1/(2^n)
Group them together as:
1/2 + (1/3 + 1/4) + .... + ( 1/(2^(n-1) +1 ) + 1/(2^(n-1)+ 2) ... + 1/(2^n)) > 1/2 + 1/2 + 1/2 ... + 1/2=n/2
S - 1 + 1/(2^n) = 1/2 + 1/3 + 1/4 ... + 1/(2^n)
Group them together as:
1/2 + (1/3 + 1/4) + .... + ( 1/(2^(n-1) +1 ) + 1/(2^(n-1)+ 2) ... + 1/(2^n)) > 1/2 + 1/2 + 1/2 ... + 1/2=n/2
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