Does the Ratio Test Confirm Divergence for This Series?

ani9890
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Ratio Test, SUPER URGENT, help?

Consider the series
∑ n=1 to infinity of asubn, where asubn = [8^(n+4)] / [(8n^2 +7)(5^n)]
use the ratio test to decide whether the series converges. state what the limit is.

From the ratio test I got the limit n-> infinity of
[8^(n+1+4)] / [(8(n+1)^2 +7)(5^n+1)] / [8^(n+4)] / [(8n^2 +7)(5^n)]
= [8^n+5(8n^2 + 7)5^n] / (8(n+1)^2 +7)5^(n+1) (8^n+4)
=[8^n(8^5)(8n^2 + 7) 5^n] / (8n^2 + 16n + 15)(5^n)(5)(8^n)(8^4)

the lim n-> infinity of [262144n^2 +229376] / [163840n^2 + 327680n + 307200]
= 8/5
which is divergence. Is this correct?

Help?
 
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ani9890 said:
Consider the series
∑ n=1 to infinity of asubn, where asubn = [8^(n+4)] / [(8n^2 +7)(5^n)]
use the ratio test to decide whether the series converges. state what the limit is.
Is this the series you're working with ?

\displaystyle \sum_{n=1}^{\infty} \frac{8^{n+4}}{(8n^2 +7)(5^n)}
From the ratio test I got the limit n-> infinity of
[8^(n+1+4)] / [(8(n+1)^2 +7)(5^n+1)] / [8^(n+4)] / [(8n^2 +7)(5^n)]
= [8^n+5(8n^2 + 7)5^n] / (8(n+1)^2 +7)5^(n+1) (8^n+4)
=[8^n(8^5)(8n^2 + 7) 5^n] / (8n^2 + 16n + 8)(5^n)(5)(8^n)(8^4)

the lim n-> infinity of (32775) / 16n + 4109 = 0
which is absolute convergence. But that answer is wrong.

Help?
Are you saying your result is wrong because the series doesn't converge absolutely?
 


yes, that is the series I'm working with.

And actually, I've redone the problem and edited my work above.
Now I got a limit of 8/5 = 1.6 so the series diverges.
Is this correct (did I calculate the limit correct)?
 


ani9890 said:
yes, that is the series I'm working with.

And actually, I've redone the problem and edited my work above.
Now I got a limit of 8/5 = 1.6 so the series diverges.
Is this correct (did I calculate the limit correct)?

Yes, that would be correct.
 
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