Sigma Notation and Series

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What is Sigma Notation?

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Sigma notation is a mathematical notation used to represent the sum of a sequence of terms. It uses the Greek letter Sigma (Σ) to indicate summation.

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What does the index in Sigma notation represent?

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The index in Sigma notation represents the variable that changes as you sum the terms. It typically starts at a lower limit and goes to an upper limit.

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How do you evaluate a sum in Sigma notation?

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To evaluate a sum in Sigma notation, substitute the index values into the expression for each term, then add the results together.

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What is the formula for the sum of the first n natural numbers?

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What is the difference between finite and infinite series?

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A finite series has a limited number of terms, while an infinite series continues indefinitely.

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What is a geometric series?

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A geometric series is a series where each term after the first is found by multiplying the previous term by a constant called the common ratio.

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What is the formula for the sum of a geometric series?

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What is an arithmetic series?

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An arithmetic series is a series where each term after the first is found by adding a constant called the common difference.

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What is the formula for the sum of an arithmetic series?

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How do you determine the number of terms in a Sigma notation?

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To determine the number of terms in Sigma notation, subtract the lower limit from the upper limit and add one.