According to the question, determine whether the given sequence converges or diverges.
The given sequence is: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} }[/tex]
Taking limits tends to infinity on both sides. And dividing numerator and denominator by [tex]n^{2}[/tex]
Therefore, the final term can be re-written as: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} } = \frac{3}{8}[/tex].
Hence, the given sequence converges and the limit is [tex]\frac{3}{8}[/tex].
What converges and diverges in limits?
When the limits of the sequence exist and have finite value that means the sequence is a convergent sequence. The calculated value is a real number. And the tem divergence means limits do not exist.
To learn more about the converges and diverges in limits from the given link:
https://brainly.com/question/15825587
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