Limits of convergent sequences

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SUMMARY

The limit of the convergent sequence defined by the formula an = (n/(n+2))^n converges to 1/e^2. Initial confusion arose regarding the divergence of the sequence, with a misinterpretation leading to the incorrect conclusion that an approaches infinity. The correct approach involves recognizing the limit behavior of the sequence as n approaches infinity, confirming its convergence to the specified limit.

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cathy
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Homework Statement



an= (n/n+2)^n

ANS: 1/e^2

The Attempt at a Solution



I was told this was convergent and I need to find the limit of the sequence. How do I do this, as I seem to keep getting that this is divergent. Isn't it divergent to infinity? Or am I missing something?
 
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Actually, this was silly of me. I figured it out.
 
Good. But as a reminder, ##\frac n n +2 = 1+2 = 3## so ##a_n = 3^n##. If you meant something else you should either use Latex or use proper parentheses.
 
Last edited:

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