This question asks whether the problem is converging (find limit) or diverging.
an= (n)^5n/(n-8)^5n
I first took the natural log of both the numerator and denominator and got ln(n)/ln(n-8), and then used l'hospitals rule to get a complicated mess. Can anyone give me some input on what went wrong, or if I just started out in the incorrect manner.
Thanks
Thanks for the help and feedback, I really appreciate it. This is the only problem out of the sequences homework that I really couldn't understand. Actually, I am still not quite sure how you came up with your solution. Could you expand on the method more or tell me where I could find out more about it?
Thanks
I don't know from your reply which part of my answer isn't understandable for you. So here is the complete version:
...... Both powers have the same exponent so they could be collected to a single base.
By the "property of a fraction" I mean: If the denominator increases the complete fraction decreases. That explains the ">"-sign.
Since this explains the equal relation in when you are going to determine the limit.
Now calculate the limit:
If approaches then approaches too.
Therefore . Replace n with 8t and keep in mind that
I really have no idea, about this convergence topic, but... im trying to understand your solution step by step.... hmmm sir, may I ask, how did you use synthetic division to make (n/(n-8))^5n into (1 -(8/n-8))^5n? I really appreciate if you could explain it to me... hmmm oh yeah.. how did you use the concept of property of fraction to make 8/n-8 to 8/n? thank you very much...
Wow! Thanks for the detailed steps for this problem. I am still puzzled as to what you did, for example the synthetic division and property of fractions. I don't ever remember learning this particular method. Is it possible to use L'hospital's rule? For example, this problem is also the same as (n/n-8)^5n, so couldn't you use the natural logarithm and then l'hospitals rule?
There are several possible ways to do the transformation:
orThis is synthetic division as it is taught in Germany.Code:8 n ÷ (n - 8) = 1 + ----- -(n - 8) n - 8 -------- 8
You probably have noticed that . So when I changed the denominator to n the denominator was enlarged by 8. Thus the value of the whole fraction became smaller. That's all.hmmm oh yeah.. how did you use the concept of property of fraction to make 8/n-8 to 8/n? thank you very much...