How is this product of terms calculated?

In summary, the product shown in the conversation is a result of taking the product of 36 different factors, where the index sign ensures that only certain pairs are allowed. The total number of factors in the product is 36, and the set over which the product is taken includes all pairs (j,i) where j and i range from 1 to 6 and i is not equal to j.
  • #1
crv357
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##\prod_{j \neq i}^{6} (\lambda_{i}-\lambda_{j})##
 
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  • #2
crv357 said:
##\prod_{j \neq i}^{6} \frac{\lambda_{i}}{\lambda_{i}-\lambda_{j}}##
We require you to at least show your thoughts. To help you get started, there are 36 different pairs (i , j) pairs where i and j range between 1 and 6. Some of these pairs aren't going to be allowed in the product above. So how many factors will there be in the product?
 
  • #3
The index sign ##j \neq i## means that you take the product over all pairs ##(j,i)## in the set ##\{(j,i): 1\leq j,i \leq 6, i \neq j\}##. For example ##(1,2)## and ##(2,1)## are elements of this set, but ##(1,1)## is not.
 
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Related to How is this product of terms calculated?

1. How do you calculate the product of terms?

The product of terms is calculated by multiplying all the terms together. For example, if you have the terms 2, 3, and 4, the product of terms would be 2 x 3 x 4 = 24.

2. What is the purpose of calculating the product of terms?

The product of terms is used to find the total value of a set of terms. It is often used in mathematical equations and formulas to simplify and solve problems.

3. Can the product of terms be negative?

Yes, the product of terms can be negative. When multiplying an odd number of negative terms, the product will be negative. For example, -2 x -3 = 6.

4. How is the product of terms different from the sum of terms?

The product of terms is the result of multiplying all the terms together, while the sum of terms is the result of adding all the terms together. The product gives the total value of the terms, while the sum gives the total quantity of the terms.

5. Can the product of terms be calculated for non-numerical terms?

Yes, the product of terms can be calculated for non-numerical terms, such as variables or algebraic expressions. The same principle of multiplying all the terms together applies, but the resulting product may be a combination of numbers and variables.

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