It has been known that the series
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diverges as n -> ∞
Now, given a positive real value k >= 1, find, if any, a general expression of n in terms of k such that
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Series inequality
2008-12-31 11:07 pm
回答 (4)
2009-01-13 7:00 am
✔ 最佳答案
竟然連n>=e^k都答得出？別忘記n必定是整數。
2009-01-12 23:00:51 補充：
圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/crazyseries/crazyseries1.jpg
圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/crazyseries/crazyseries2.jpg
圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/crazyseries/crazyseries3.jpg
圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/crazyseries/crazyseries4.jpg
圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/crazyseries/crazyseries5.jpg
參考資料：
My Maths knowledge
2009-04-04 5:10 am
2009-01-15 7:47 pm
以 k = 3 為例, 當 n = 11 時已經個 sum > 3
但 e^3 = 20.1, 即 n 要 = 21, 所以 n >= e^k 並不正確.
但 e^3 = 20.1, 即 n 要 = 21, 所以 n >= e^k 並不正確.
2008-12-31 11:30 pm
ln(n+1)=int{from 1 to n+1} 1/x dx <= sum{i=1 to n} 1/i
so, choose n such that ln(n+1)>=k is enough
so n>=e^k-1
so just choose n>=e^k
so, choose n such that ln(n+1)>=k is enough
so n>=e^k-1
so just choose n>=e^k
收錄日期: 2021-04-19 13:16:13
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081231000051KK01135