$$\sum_{n=1}^{\infty} \frac{sin4n}{{4}^{n}}$$

doing the ratio test

$$ \lim_{n \rightarrow \infty} \left| \frac{\frac{sin4(n+1)}{{4}^{n+1}}}{\frac{sin4n}{{4}^{n}}} \right|$$

here is how far i got

$$ \lim_{n \rightarrow \infty} \left| \frac{sin4(n+1)}{sin4n} + \frac{1}{4} \right|$$

Question

$$\sum_{n=1}^{\infty} \frac{sin4n}{{4}^{n}}$$

doing the ratio test 

$$ \lim_{n \rightarrow \infty} \left| \frac{\frac{sin4(n+1)}{{4}^{n+1}}}{\frac{sin4n}{{4}^{n}}} \right|$$  

here is how far i got

$$ \lim_{n \rightarrow \infty} \left| \frac{sin4(n+1)}{sin4n} + \frac{1}{4} \right|$$

anonymous · Answer

instead of + you should put *

anonymous · Answer

thanks...sorry

anonymous · Answer

and this ratio is not correct for that because it has not limit.

anonymous · Answer

it's not convergent because it's $$\infty $$ ?

anonymous · Answer

you should solve it with comparing known model.

anonymous · Answer

it is convergent .it obviously is !

anonymous · Answer

is it because you did a comparison test?

anonymous · Answer

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