F.4 limit questions

2008-08-20 2:55 am
1. lim n>infinity (1+2+3+..+n)/n^2
Why we can't treat as 1/n^2+ 2/n^2+..+1/n and then equal 0?

2. lim n>infinity (1+1/2+1/4+...+1/2^n)

3. lim x>infinity ( (x^3+x)^1/3 - (x^3+3)^1/3 )

回答 (1)

2008-08-20 5:01 am
✔ 最佳答案
As follows:

圖片參考:http://hk.geocities.com/stevieg_1023/0l2.gif


2008-08-19 21:03:43 補充:
Why we can't treat as 1/n^2+ 2/n^2+..+1/n and then equal 0?

If we do so , then it becomes 0+0+.......0}n terms of 0 , but n tends to infinity ,
that is ∞ * 0 , which is an undeterminate form .


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