1. ## Infinite Sequences

I'm hoping someone can help me out with a couple problems. For both of them, I need to determine if the sequence is convergent or divergent, and if it is convergent, I need to find the limit:

1. a(sub n) = (5^n+2)/(7^n)

2. a(sub n) = sqrt of (n+1)/(9n+1)

Anyone have any ideas or suggestions??

2. Originally Posted by Jessica098
I'm hoping someone can help me out with a couple problems. For both of them, I need to determine if the sequence is convergent or divergent, and if it is convergent, I need to find the limit:

1. a(sub n) = (5^n+2)/(7^n)

2. a(sub n) = sqrt of (n+1)/(9n+1)

Anyone have any ideas or suggestions??
1. Is it $a_n = \frac{5^n + 2}{7^n}$ or $a_n = \frac{5^{n + 2}}{7^n}\,$?

2. Note that $\frac{n+1}{9n+1} = \frac{1 + \frac{1}{n}}{9 + \frac{1}{n}}$ .......

3. It's

4. Originally Posted by Jessica098
It's
Then $a_n = 25 \, \left( \frac{5}{7} \right)^n$ ......

(You know $\lim_{n \rightarrow +\infty} \left( \frac{5}{7} \right)^n = 0$, right?).

5. Originally Posted by Jessica098
It's
Yes. I know. I read it the first time.

Do you understand that $5^{n+2} = 5^n \times 5^2 = 5^n \times 25 = 25 (5^n)$ ? Now go back and read my previous reply again.

6. Originally Posted by Jessica098
It's
Perhaps it would be more efficient for you if, instead of simply repeating yourself, you told Mr. F. what exactly it is about his help you are not able to follow.

-Dan