# Does the Numerical Solution for the Equation Converge?

• atomqwerty
In summary, the conversation discusses finding a numerical solution for the equation n - m - a*r - 5*log(r) = 0 and proving that the procedure given for finding the solution converges. The equations are rewritten and variables are identified, and numerical methods are suggested for finding the solution. The question is how to demonstrate the convergence of the solution.
atomqwerty

## Homework Statement

Let be the equation

n - m - a*r - 5*log(r) = 0

## Homework Equations

We proceed by rewritting

n - m - a*r = 5*log(r)

Now we have separate equations, which variables we identificate as

n - m - a*x = 5*log(y)

Since we need a numerial solution, we apply numerical methods, like
c
x=0 -> y0
x=y0 -> y1
x=y1 -> y2
...

The question is to probe that the solution converges. I don't know how to satrt this!

so what are you trying to do

find the zeros wrt r of:
n - m - a*r - 5*log(r) = 0...?

lanedance said:
so what are you trying to do

find the zeros wrt r of:
n - m - a*r - 5*log(r) = 0...?

I'm trying to figure out a numerical solution for this particular equation, and I've been asked to demonstrate that the procudure I wrote down above converges, i.e, that gives a non-infinite solution.

## 1. What does it mean for a sequence to converge?

Convergence in a sequence means that as the sequence progresses, the values get closer and closer to a single number. In other words, the limit of the sequence exists.

## 2. How can you prove that a sequence converges?

To prove that a sequence converges, you can use various methods such as the squeeze theorem, the Cauchy criterion, or the monotone convergence theorem. These methods involve showing that the sequence is bounded and/or decreasing/increasing towards a specific limit.

## 3. Can a sequence converge to more than one limit?

No, a sequence can only converge to one limit. If a sequence has more than one limit, it is considered divergent.

## 4. What is the difference between absolute and conditional convergence?

Absolute convergence means that the series converges regardless of the order in which the terms are added. Conditional convergence, on the other hand, means that the series only converges when the terms are added in a specific order.

## 5. How does the speed of convergence affect the convergence of a sequence?

The speed of convergence refers to how quickly the values in a sequence approach the limit. Generally, a sequence with a faster convergence rate is considered to have a better convergence compared to a sequence with a slower convergence rate.

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