- #1
steve2212
- 11
- 0
Homework Statement
Find the limit of the sum of:
y = (2n + 3n) / 4n
The Attempt at a Solution
as n-> infinity, y approaches 0. I don't know where to proceed from here.
Dick said:It's 2^n/4^n+3^n/4^n=(2/4)^n+(3/4)^n. It's two separate geometric series. Can you deal with those?
steve2212 said:Ya I got that but I don't know how to find the sum of an infinite geometric series
steve2212 said:Oh sorry I'm stupid, I remembered how haha.
Since you're here I also have another hard one.
A circle is inscribed in a triangle, a square is inscribed in that circle, a circle is inscribed is that square, a pentagon is inscribed in that circle, the trend continues with the degree going up.
How do I proceed to solve this quesiton? I need to find t he sum of the limit
steve2212 said:The limit of the sum of the area. Sorry forgot that detail.
Dick said:How do you know the areas approach zero? Sure, they decrease. But that doesn't convince me that they approach zero. Do you know this has a simple solution? Because I'm sure not seeing it.
steve2212 said:Area can't be negative, and area decreases, it has to approach 0. Right?
steve2212 said:Sorry where do you get 1+ 1/n?
The sum of an infinite series is the total value obtained by adding up an infinite number of terms. This is often represented by the symbol ∑, which stands for "sum". Infinite series are important in mathematics and physics, as they can be used to approximate values and solve equations.
The sum of an infinite series is calculated using a specific formula or method, depending on the type of series. Some common methods include the geometric series formula, the telescoping series method, and the ratio test. It is important to note that not all infinite series have a finite sum.
A convergent series is an infinite series that has a finite sum. This means that the total value obtained by adding up all the terms in the series is a real number. Convergent series are important in calculus and are used to evaluate integrals and solve differential equations.
A divergent series is an infinite series that does not have a finite sum. This means that no matter how many terms are added, the total value will continue to increase or decrease without ever reaching a fixed value. Divergent series can be used in certain mathematical proofs and also have applications in physics.
Infinite series have many practical applications in real life, particularly in the fields of mathematics, physics, and engineering. They are used to approximate values and solve equations, and can also be used to model real-world phenomena such as population growth, financial investments, and electrical circuits. Infinite series also play a role in computer science and data analysis.