Originally Posted by

**kspkido** 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...

There are several possible ways to do the transformation:

$\displaystyle \frac{n}{n-8} = \frac{n-8+8}{n-8} = \frac{n-8}{n-8}+\frac8{n-8} = 1+\frac{8}{n-8}$

or Code:

8
n ÷ (n - 8) = 1 + -----
-(n - 8) n - 8
--------
8

This is synthetic division as it is taught in Germany.

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...

You probably have noticed that $\displaystyle n - 8 < n$. 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.