I'm not sure why the lim as n goes to infinite of ln(n)/ln(n+1) is 1.
If you take the l'hopital's rule you get (1/n)/(1/(n+1)).
(1/n) goes to 0, and 1/(n+1) also goes to zero.
Shouldn't the limit be 0?
Why is the limit of ln(n)/ln(n+1) 1?
2017-04-26 4:35 am
回答 (3)
2017-04-26 5:58 am
As n approaches ∞, n = n+1.
2017-04-26 5:52 am
Use l'hopital rule
lim n->oo ln(n)/ln(n+1)
= (1/n) / (1/n+1)
= 1
lim n->oo ln(n)/ln(n+1)
= (1/n) / (1/n+1)
= 1
2017-04-26 4:45 am
AHH , but [ 1 / n ] / [ 1 / ( n + 1 ) ] ≡ ( n + 1 ) / n ≡ 1 + 1/n...don't forget your grade school arithmetic
收錄日期: 2021-04-24 00:23:15
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170425203505AAFpicj