This question asks whether the problem is converging (find limit) or diverging.
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.
...... 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...
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...