Sigma Notation

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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 numbers, typically expressed using the Greek letter sigma (Σ).

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What does the symbol Σ represent in Sigma Notation?

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The symbol Σ represents the sum of a series of terms.

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How do you interpret the expression Σ (from i=1 to n) of a_i?

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This expression means to sum the terms a_i from i=1 to n, where 'i' is the index of summation.

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

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The formula is S = n(n + 1)/2.

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What is the sum of the series Σ (from i=1 to 5) of i?

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The sum is 15, calculated as 1 + 2 + 3 + 4 + 5.

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How do you calculate Σ (from i=1 to n) of i^2?

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The formula is S = n(n + 1)(2n + 1)/6.

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What is the sum of the series Σ (from i=1 to 4) of i^2?

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The sum is 30, calculated as 1^2 + 2^2 + 3^2 + 4^2.

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What does it mean if a series converges?

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A series converges if the sum of its terms approaches a finite limit as the number of terms increases.

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What is an example of a divergent series?

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The series Σ (from n=1 to ∞) of 1/n diverges, as it does not approach a finite limit.

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What is the difference between a finite series and an infinite series?

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