## Loser66 one year ago $$lim_{n\rightarrow \infty} |\dfrac{1}{a^{2n+1}|}=??$$ Please, help

1. misty1212

gotta be zero right?

2. misty1212

denominator goes to $$\infty$$ lickety split

3. Loser66

This is what I got, but need the third party's opinion. |dw:1443275074358:dw|

4. misty1212

oh i guess i didn't take in to account the possibility that $$a=1$$ did i?

5. Loser66

I don't feel good for the first one and the last one. They should be combined to make the logic firmly.

6. misty1212

if $$a=1$$ then it is identically 1

7. misty1212

if $$0<a<1$$ it is $$\infty$$ since the denominator goes to $$0$$

8. misty1212

and like you said if $$a>1$$ it would be $$0$$ because the denominator gets really big really fast

9. misty1212

looks good to me!

10. Loser66

|dw:1443275584269:dw|

11. Loser66

Another question: $$lim_{n\rightarrow \infty} a^n z^n$$ , what is difference if a is in Z and a is in C ?