Confused About Infinity: Help Understanding a Math Limit

In summary, the limit of n(n+1)/2n^2 as n approaches infinity is equal to 1/2. This is because n(n+1)/2n^2 can be simplified to 1/2 + 1/2n, and as n approaches infinity, 1/2n approaches 0, resulting in a final value of 1/2. This is also due to the fact that 1/(2n) can be factored out of the limit, resulting in a constant value of 1/2.
  • #1
danne89
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My book tolds me that: [tex]\lim_{n\rightarrow\infty} \frac{n(n+1)}{2n^2}= \frac{1}{2}[/tex]. I don't get it. Maybe this with infinity, I dunno... Please, help!
 
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  • #2
Because

[tex] \frac{n(n+1)}{2n^2} = \frac{n^2+n}{2n^2} = \frac{n^2}{2n^2} +\frac{n}{2n^2} = \frac{1}{2} + \frac{1}{2n} [/tex]
 
  • #3
Ok, I think I got it now. So it's based on that 1/n equals 0, when n approaches infinity and 2 * infinity = infinity, right?
 
  • #4
danne89 said:
Ok, I think I got it now. So it's based on that 1/n equals 0, when n approaches infinity and 2 * infinity = infinity, right?

yeah, the 1/(2n)=(1/2)(1/n) so you can factor the constant out of the limit, ie lim (1/(2n)) = (1/2) * lim (1/n) --> 0 as n --> infinity
 

FAQ: Confused About Infinity: Help Understanding a Math Limit

What is a math limit?

A math limit is a concept in calculus that represents the value that a function approaches as its input approaches a specific value. It is used to describe the behavior of a function near a particular point.

What is infinity?

Infinity is a concept that represents something without any limit or end. In math, it is often used to describe numbers that are infinitely large or infinitely small.

What does it mean to be "confused about infinity"?

Being confused about infinity means having difficulty understanding the concept of infinity and its applications in math. It can also refer to having trouble grasping the concept of approaching infinity in math limits.

How can I understand infinity better?

To understand infinity better, it is important to have a solid foundation in basic math concepts, such as numbers and operations. It can also be helpful to study and practice with different types of infinity, such as cardinal and ordinal infinity, and to explore real-life examples of infinity, such as the concept of forever.

What are some tips for understanding math limits involving infinity?

Some tips for understanding math limits involving infinity include understanding the concept of approaching infinity, using algebraic and graphical methods to solve limits, and practicing with different types of limits, such as indeterminate forms. It can also be helpful to seek additional resources, such as textbooks and online tutorials, for further clarification and practice.

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