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Questions and Answers
Which of the following statements about summation notation is true?
Which of the following statements about summation notation is true?
- The summation of a constant with the index set is equal to the product of the constant and the number of terms in the index set. (correct)
- The summation of the product of a constant with a variable is equal to the product of the constant with the summation of the variable.
- The summation of the sum of two terms is equal to the sum of the individual summations.
- The summation of a constant with the index set is equal to the constant.
What does the index of summation represent?
What does the index of summation represent?
- The upper limit of summation
- The lower limit of summation
- The value of the variable for the ith observation (correct)
- The collection of consecutive integers from the lower limit to the upper limit of summation
What is the upper limit of summation?
What is the upper limit of summation?
- The collection of consecutive integers from the lower limit to the upper limit of summation (correct)
- The index of summation
- The value of the variable for the ith observation
- The lower limit of summation
Which property of summation allows us to distribute a constant outside the summation?
Which property of summation allows us to distribute a constant outside the summation?
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What does the term of the summation represent?
What does the term of the summation represent?
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Study Notes
Summation Notation Overview
- A concise mathematical notation representing the sum of a sequence of terms.
- Summation notation is typically denoted by the Greek letter Sigma (Σ).
Index of Summation
- Represents the variable of summation; it indicates the position of each term in the sequence.
- The index often starts at a specific value and increments by one until it reaches the upper limit.
Upper Limit of Summation
- The maximum value that the index of summation can take.
- It determines the total number of terms to be included in the summation.
Distributing a Constant
- The property of summation that allows a constant factor to be factored out is known as the linearity of summation.
- This property states that c * Σa_n = Σ(c * a_n), where c is a constant and a_n is the term being summed.
Term of the Summation
- Represents each individual element or component being added together in the summation.
- The term is typically defined by the index, such as a_i for i = 1 to n, indicating that each term corresponds to a different value of the index.
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