# Thread: ratio test (series) urgent help

1. ## ratio test (series) urgent help

hey i m not sure if i did the right if anyone can help

2. Originally Posted by Legendsn3verdie
hey i m not sure if i did the right if anyone can help
We need to fidn $\displaystyle \lim\left|\frac{a_{n+1}}{a_n}\right|$

So now if $\displaystyle a_{n}=5\cdot 5^{-n}$ then $\displaystyle a_{n+1}={\color{red}5}\cdot 5^{-n+1}$

So your limit is $\displaystyle \lim_{n\to\infty}\frac{5\cdot{5^{-n}}}{5\cdot{5^{-n+1}}}=\frac{1}{5}<1$ thus convergent.

3. Notice that your series is a geometric series.

4. Originally Posted by Mathstud28
We need to fidn $\displaystyle \lim\left|\frac{a_{n+1}}{a_n}\right|$

So now if $\displaystyle a_{n}=5\cdot 5^{-n}$ then $\displaystyle a_{n+1}={\color{red}5}\cdot 5^{-n+1}$

So your limit is $\displaystyle \lim_{n\to\infty}\frac{5\cdot{5^{-n}}}{5\cdot{5^{-n+1}}}=\frac{1}{5}<1$ thus convergent.
whoa wut u did there mad me realize what i probably did wrong.. can u vouch if this is correct. i wrote my change in green:

5. Originally Posted by Legendsn3verdie
whoa wut u did there mad me realize what i probably did wrong.. can u vouch if this is correct. i wrote my change in green:

Perfect