Limit of a Series as n Approaches Infinity: Exploring Convergence and Divergence

  • Thread starter mathpat
  • Start date
  • Tags
    Limit
In summary, finding the limit of s(n) as n approaches infinity means determining the value that s(n) approaches as n gets larger and larger. This can be calculated using various methods and is important in understanding the long-term behavior of a sequence or function. The limit can be undefined if the sequence does not approach a specific value, and it has real-world applications in fields such as physics, engineering, and economics.
  • #1
mathpat
15
0

Homework Statement



Find the limit of s (n) as n →∞ s(n) = Ʃ n, i = 1. (10i - n) /(n^2)


Homework Equations



n/a

The Attempt at a Solution



I am completely stumped. I've read my textbook multiple times. I don't even know how to approach these type of problems. I am so confused. Can anyone guide me?
 
Physics news on Phys.org
  • #2
Can you show a scan or photo of the problem in your book?

ehild
 

FAQ: Limit of a Series as n Approaches Infinity: Exploring Convergence and Divergence

1. What does it mean to find the limit of s(n) as n approaches infinity?

Finding the limit of s(n) as n approaches infinity means determining the value that s(n) approaches as n gets larger and larger. This can be thought of as the "end behavior" of s(n) or the value that the sequence approaches as n becomes infinitely large.

2. How is the limit of s(n) as n approaches infinity calculated?

The limit of s(n) as n approaches infinity is calculated by taking the limit of the function s(n) as n goes to infinity. This can be done using various methods such as algebraic manipulation, graphing, or using mathematical tools like L'Hôpital's rule or the squeeze theorem.

3. What is the significance of finding the limit of s(n) as n approaches infinity?

Finding the limit of s(n) as n approaches infinity is important in understanding the long-term behavior of a sequence or function. It can also be used to determine the convergence or divergence of a series, and to make predictions about future values of a sequence.

4. Can the limit of s(n) as n approaches infinity be undefined?

Yes, the limit of s(n) as n approaches infinity can be undefined. This can happen if the sequence does not approach a specific value or if it oscillates between different values as n gets larger. In this case, the limit is said to be "infinity" or "negative infinity" depending on the direction of the oscillation.

5. How is finding the limit of s(n) as n approaches infinity useful in real-world applications?

Finding the limit of s(n) as n approaches infinity can be useful in various real-world applications such as physics, engineering, and economics. It can be used to model and predict the behavior of systems that involve continuous growth or decay, such as population growth or radioactive decay. It can also be used to optimize processes and make informed decisions based on long-term trends.

Similar threads

Replies
8
Views
1K
Replies
24
Views
1K
Replies
2
Views
1K
Replies
4
Views
606
Replies
16
Views
1K
Replies
2
Views
1K
Back
Top