# What is wrong with my summation formula?

• DerekZ10
In summary, the conversation is about finding a formula to calculate the number of onto (surjective) functions for a relation between two sets, M and N, using a calculator. The person has developed a formula but it does not match with a problem they found on Google. They realize that there was a mistake in their formula and make the necessary corrections.
DerekZ10
Im trying to find a general formula I can store in my calculator that can find the number of onto (surjective) functions exists for a relation of when M is mapped to N.

I can't seem to find a nice formula for it, but based on the below material I will show you what I have developed.

From: Discrete Mathemeatics and Its Applications 7th Edition Rosen pg. 561
From: Discrete Mathemeatics and Its Applications 7th Edition Rosen pg. 512

Random Chegg Problem from Google Search I'm using to verify with:
Here is what I've formed, written out:

In the TI nSpire CX CAS, it's written like this:

And as you can see, the chegg problem I'm trying to verify it with doesn't match!
But I think it should! If I manually iterate the function like so:

The values are correct and what Chegg is showing. What have I done wrong in my equation?

Did you check that your summation formula matches the version that doesn't use sigma notation? i.e are all your ##m##s and ##n##s where they're supposed to be?

1 person
Wow, good call! I don't know how I constantly was missing that the (m-k) portion that should have been (n-k). And I even had it right in the non iterative equation.

## What is wrong with my summation formula?

There could be several reasons for a summation formula to be incorrect. Some common issues include:

## Why is my summation formula giving me the wrong answer?

There may be a mistake in your formula, such as using the wrong mathematical operation or forgetting to include a term. It is also possible that there is an error in the data you are using, or that you are using the formula in the wrong context.

## How can I check if my summation formula is correct?

One way to check the accuracy of your summation formula is to manually calculate the sum for a few values and compare it to the result of your formula. You can also use a spreadsheet or calculator to verify the answer.

## What should I do if my summation formula is still not working?

If you have checked your formula and it still does not give the expected result, try breaking it down into smaller parts and testing each one individually. It may also be helpful to ask a colleague or consult a textbook or online resource for assistance.

## How can I improve the accuracy of my summation formula?

If you are consistently getting incorrect results with your summation formula, consider double-checking your data and formula for errors. You may also want to use more precise or advanced mathematical techniques, such as integrating or differentiating your summation formula, to improve its accuracy.

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