# Can I use this formula to simplify my summations?

• Luongo
In summary, the conversation discussed how to multiply a summation in a homework problem involving dummy variables. The speaker suggests replacing the variable in the second summation with a different letter and then applying a formula to solve the problem.

#### Luongo

1. on #1 c) of the homework:
http://www.math.ubc.ca/~oyilmaz/courses/m267/hmk3.pdf [Broken]
how do i multiply this summation?

## Homework Equations

3. what i did was i multiplied the 2 expos and made on of the k indexes a 'm' instead and i got $$\sum ei(k+m)t$$

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$$\left( \sum_{k =1}^{N_1} f(k) \right) \left( \sum_{j=1}^{N_2} g(j) \right) = \sum_{k=1}^{N_1} \sum_{j=1}^{N_2} f(k)g(j)$$

Can you try to see why the above is true?

Now in your problem, k is a dummy variable (meaning, that since it sums over, it doesn't matter if we call it k, or j). So we can replace the variable in the second summation, by j. Then you can apply the above formula.

## 1. What is the purpose of multiplying summations?

Multiplying summations is a mathematical operation used to find the product of two or more summations. It is commonly used in scientific and engineering calculations to simplify large and complex equations.

## 2. How do I multiply two summations?

To multiply two summations, you need to use the distributive property and multiply each term in one summation by each term in the other summation. Then, you can combine like terms to find the final product.

## 3. Can I multiply more than two summations at once?

Yes, you can multiply any number of summations together. However, as the number of summations increases, the complexity of the calculation also increases.

## 4. What are some practical applications of multiplying summations?

Multiplying summations is commonly used in fields such as physics, engineering, and finance. It can be used to calculate things like the total energy of a system, the value of an investment over time, or the displacement of an object under the influence of multiple forces.

## 5. Are there any special rules for multiplying summations?

Yes, there are a few special rules to keep in mind when multiplying summations. For example, the order of multiplication does not matter, and you can use the associative and commutative properties to rearrange the terms. Additionally, if one summation has an index that is a constant, it can be factored out of the product.