- #1
Firepanda
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I believe the second is simply 1, as I can ignore a here.
Not sure about the first, I believe it tends to 0 because of the power of n, and (n/n+1) < 1
Any help appreciated, thanks!
TheFurryGoat said:For the first:
First of all, you need to fiddle around with the expression so that you get something you recognize. Now
n/(n+1) = 1 / ( (n+1)/n ) = 1 / ( (1+1/n) ),
so if you plug this in the original you get
( 1 / ( (1+1/n) ) )^n = 1 /( ( (1+1/n) ) )^n
and now you should recognize the limit of this.
The limit as n approaches infinity refers to the value that a function or sequence approaches as the input approaches infinity. In other words, it is the value that the function or sequence gets closer and closer to, but never reaches, as the input gets larger and larger.
The limit as n approaches infinity can be calculated by evaluating the function or sequence at increasingly larger values of n. If the values of the function or sequence are approaching a specific number, that number is the limit. If the values are approaching infinity or negative infinity, the limit does not exist.
If the limit as n approaches infinity does not exist, it means that the function or sequence does not approach a specific value as the input gets larger and larger. This could happen if the function or sequence oscillates between different values or if it approaches positive and negative infinity at different rates.
Yes, the limit as n approaches infinity can vary depending on the specific function or sequence. Some functions or sequences may approach a specific value as n gets larger, while others may approach infinity or negative infinity. It is important to evaluate each function or sequence individually to determine its limit as n approaches infinity.
Finding the limit as n approaches infinity is useful in many areas of mathematics, physics, and engineering. It can be used to model real-world situations, such as the growth rate of a population over time or the behavior of a particle as it approaches the speed of light. It can also help in solving complex equations and understanding the behavior of functions and sequences at extreme values.