# How Do Recursion Formulas Work in Mathematics?

• skrying
In summary, the conversation is about studying recursion formulas and how they work. The main focus is on the formula a_n = 1/2^n, which can be rewritten and has no limit on the value of n. The conversation ends with gratitude for the help and understanding of the formula.
skrying
Hi everyone,

Right now my class is studying recursion formulas - er, when the next answer is based off the answer before it, if that makes any sense? I am having a hard time understanding this.

A picture of the attached problem is included...Thanks for any and all help for this problem.

skrying

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• Recursion Formula.bmp
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That is a geometrical progression.The "n+1" term is gotten from the "n"-th by dividing through 2.

It converges to 0.What else...?

Daniel.

skrying said:
Hi everyone,

Right now my class is studying recursion formulas - er, when the next answer is based off the answer before it, if that makes any sense? I am having a hard time understanding this.

A picture of the attached problem is included...Thanks for any and all help for this problem.

skrying

You have:
$$a_n=\frac{1}{2^n}$$

That's just an expression for the n'th term. Something like:

$$a_n=2a_{n-1}+3a_{n-2}$$

would be a recursive formula defining the n-th term as a function of the n-1 term and the n-2 term.

Last edited:
Thanks Dexter and Salty

Thank you dexter and salty for your input. It does make more sense when you put it that way. I think I am just making all this harder than it really is perhaps?

Thanks, Skrying

How far can this recursion formula go?

I had another quick question (and probably a dumb one) since math of any kind is not my forte'...how far does or can this formula continue..?

Thanks!

skrying said:
I had another quick question (and probably a dumb one) since math of any kind is not my forte'...how far does or can this formula continue..?

Thanks!

What Dexter was saying is

$$a_n = \frac{1}{2^n}$$

can be rewritten. Since

$$a_{n-1} = \frac{1}{2^{n-1}}$$

$$a_n = \frac{1}{2^n} = \frac{1}{2 \bullet 2^{n-1}}=\frac{1}{2} a_{n-1}$$

That is the recursion formula, and it goes on forever. There is no limit on the value of n.

Thank you OlderDan

Thanks OlderDan...that looks like the same way some of my classmates were working on the problem. I really appreciate your help!

Thanks Skrying!

## 1. What is a recursion formula?

A recursion formula is a mathematical formula that defines a sequence or series based on the previous terms in the sequence. It is a way to express a mathematical relationship between a term and its preceding terms.

## 2. How is a recursion formula different from a regular formula?

A recursion formula is different from a regular formula because it uses previous terms in the sequence to define the next term, whereas a regular formula uses specific values or variables to calculate the result.

## 3. What are some common examples of recursion formulas?

Some common examples of recursion formulas include the Fibonacci sequence, the factorial function, and the Tower of Hanoi problem. These are all mathematical problems that can be expressed using recursion formulas.

## 4. What are the benefits of using recursion formulas?

Recursion formulas offer a more elegant and concise way to express mathematical relationships. They also allow for the solution of complex problems that may be difficult to solve using regular formulas.

## 5. How can I solve a problem using a recursion formula?

To solve a problem using a recursion formula, you must first identify the pattern in the sequence or series. Then, you can use the recursion formula to express the relationship between the terms and use it to calculate the desired value. It may also be helpful to draw a tree diagram to visualize the recursive process.

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