# division explanation

• Sep 23rd 2011, 06:41 PM
l flipboi l
division explanation
Hello,

I was wondering... Why is it divided by $n^2$? This is actually a calculus problem, trying to determine if the series is convergent or divergent.

But, I just needed some clarification on the algebra.

Thanks,Attachment 22379
• Sep 23rd 2011, 08:03 PM
Soroban
Re: division explanation
Hello, l flipboi l!

Quote:

Why is it divided by $n^2$?

$\lim_{n\to\infty}\frac{n}{\sqrt{10+n}} \;=\;\lim_{n\to\infty}\dfrac{1}{\sqrt{\dfrac{10}{n ^2}+\dfrac{1}{n}}} \;=\;\infty$

We have the fraction: . $\frac{n}{\sqrt{10+n}}$

$\text{Divide top and bottom by }n\!:$

. . $\dfrac{\dfrac{n}{n}}{\dfrac{\sqrt{10+n}}{n}} \;=\;\dfrac{1}{\dfrac{\sqrt{10+n}}{\sqrt{n^2}}} \;=\;\frac{1}{\sqrt{\dfrac{10+n}{n^2}}} \;=\;\frac{1}{\sqrt{\dfrac{10}{n^2} + \dfrac{n}{n^2}}} \;=\;\frac{1}{\sqrt{\dfrac{10}{n^2} + \dfrac{1}{n}}}$

Got it?