# Any tips on how to conjecture formulas for Induction?

• phillyolly
In summary, when conjecturing formulas for math induction based on a given sum of sequence, there are a few tips that may be helpful. These include reversing the order and grouping terms, using the "r" of a geometric series, and utilizing clever tricks. However, there is no set procedure for coming up with these tricks, and one possible approach is through generatingfunctionology.
phillyolly
What are usual tips in conjecturing formulas for math induction if I am given a certain sum of sequence? Thank you.

It depends on the problem.

In the case of sums...

Sometimes simply reversing the order and adding it to itself and then grouping terms is sufficient.

In the case of the geometric series simply multipliying the partial sum by the "r" of the geometric series and then performing S-rS can do some magic.

Usually there is some sort or clever trick involved and no one can really give you a procedure for coming up with clever tricks.

I only "general" way of coming up with formulas of that sort is generatingfunctionology ,yes it is actually a topic. I remember coming across an online book of that sort when I wanted to find a solution to a recursive integral. I didn't have the patience to read through more than 5pages though.

## 1. How do I approach conjecturing formulas for induction?

When trying to come up with formulas for induction, it is important to carefully examine the pattern you are working with and look for any relationships or regularities. It can also be helpful to try smaller cases first and see if you can find a general rule or formula that works for all cases.

## 2. Are there any strategies or techniques that can help with conjecturing formulas for induction?

Some common strategies for coming up with formulas for induction include using algebraic manipulations, looking for similar patterns in previous examples, and working backwards from the desired result. It can also be useful to break down the problem into smaller, more manageable parts.

## 3. What should I do if I am stuck on finding a formula for induction?

If you are struggling to find a formula for induction, it can be helpful to take a break and come back to the problem with a fresh perspective. You can also try discussing the problem with others or seeking help from a mentor or teacher.

## 4. Is there a certain way to test if a conjectured formula for induction is correct?

To test a conjectured formula for induction, you can plug in different values and see if it produces the expected result. Additionally, you can use mathematical induction to prove that the formula holds true for all cases.

## 5. Are there any common mistakes to avoid when conjecturing formulas for induction?

One common mistake is assuming that a pattern seen in a few initial cases will continue to hold true for all cases. It is important to thoroughly test and prove the formula using mathematical induction. Another mistake is overlooking simpler, more elegant solutions in favor of more complex ones. It is important to carefully consider all possibilities and approaches when conjecturing formulas for induction.

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