- #1

karush

Gold Member

MHB

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Determine Convergence or divergence and test used

$\displaystyle\sum_{n=1}^{\infty} \dfrac{1+4^n}{1+3^n}$

W|A says diverges using ratio test so

$\therefore L=\lim_{n \to \infty}\left|\dfrac{a_n+1}{a_n}\right|>1$

Steps

$\displaystyle L=\lim_{n \to \infty}\left| \dfrac{1+4^{n+1}}{1+3^{n+1}}\cdot\dfrac{1+3^n}{1+4^n}\right|$ ok just seeing if I have this first step set up ok... before I run it thru the grinder..

I assume ratio test is a limit test...

View attachment 9345

$\displaystyle\sum_{n=1}^{\infty} \dfrac{1+4^n}{1+3^n}$

W|A says diverges using ratio test so

$\therefore L=\lim_{n \to \infty}\left|\dfrac{a_n+1}{a_n}\right|>1$

Steps

$\displaystyle L=\lim_{n \to \infty}\left| \dfrac{1+4^{n+1}}{1+3^{n+1}}\cdot\dfrac{1+3^n}{1+4^n}\right|$ ok just seeing if I have this first step set up ok... before I run it thru the grinder..

I assume ratio test is a limit test...

View attachment 9345

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