Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "o0" (without the quotation marks). If it diverges to negative infinity, state your answer as "-o0". If it diverges without being infinity or negative infinity, state your answer as "DNE". n2 lim T 00 e
Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "o0" (without the quotation marks). If it diverges to negative infinity, state your answer as "-o0". If it diverges without being infinity or negative infinity, state your answer as "DNE". n2 lim T 00 e
Transcribed Image Text:**Sequence Convergence or Divergence Analysis**
Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-oo". If it diverges without being infinity or negative infinity, state your answer as "DNE".
\[
\lim_{{n \to \infty}} \frac{{n^2}}{{e^{-8n}}}
\]
**Explanation:**
This expression represents the limit of the sequence as \( n \) approaches infinity. The numerator \( n^2 \) grows quadratically, while the denominator \( e^{-8n} \) involves an exponential term. As \( n \) increases, consider how these terms affect the behavior of the sequence to determine if it converges or diverges.
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![**Sequence Convergence or Divergence Analysis**
Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-oo". If it diverges without being infinity or negative infinity, state your answer as "DNE".
\[
\lim_{{n \to \infty}} \frac{{n^2}}{{e^{-8n}}}
\]
**Explanation:**
This expression represents the limit of the sequence as \( n \) approaches infinity. The numerator \( n^2 \) grows quadratically, while the denominator \( e^{-8n} \) involves an exponential term. As \( n \) increases, consider how these terms affect the behavior of the sequence to determine if it converges or diverges.](https://content.bartleby.com/qna-images/question/6cf09b2a-e92e-430b-8152-8153c73e6dd1/ec734749-30dc-48b7-a0f8-bacfd5d9678e/xx12fgc_processed.png)
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