Find Limit of Sequence: an = (1/(e^(4n)+n^2))^1/n

In summary, the formula for the given sequence is an = (1/(e^(4n)+n^2))^1/n. The limit of the sequence as n approaches infinity is 1. To find the limit of a sequence, you need to take the value of n to infinity and see what value the sequence approaches. e is a mathematical constant that is approximately equal to 2.71828. You can use a calculator to find the limit of a sequence, but it is important to understand the concept of limits and how to find them manually.
  • #1
TWM
2
0
Find the limit of the sequence whose terms are given by

an = ( [1/(e^(4n)+n^2)] )^1/n

I am not really sure how to approach this problem.

thanks!
 
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  • #2
Try the binomial expansion of denominator and apply the limits to each term (don't forget that you always can use the L'Hopital rule for those limits). I guess the that the limit is 1/e^4.
 

What is the formula for the given sequence?

The formula for the given sequence is an = (1/(e^(4n)+n^2))^1/n.

What is the limit of the sequence as n approaches infinity?

The limit of the sequence as n approaches infinity is 1.

How do you find the limit of a sequence?

To find the limit of a sequence, you need to take the value of n to infinity and see what value the sequence approaches. If it approaches a constant value, then that is the limit of the sequence.

What is e in the given sequence?

e is a mathematical constant that is approximately equal to 2.71828. It is often used in mathematical and scientific calculations.

Can you use a calculator to find the limit of the sequence?

Yes, you can use a calculator to find the limit of a sequence. You can input the formula for the sequence and then take the value of n to infinity to see what value the sequence approaches. However, it is important to note that calculators may not always give an exact answer and it is important to understand the concept of limits and how to find them manually.

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