Gr12 Mathematics: Ch 1.3 Series

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Questions and Answers

What is the definition of a series?

  • The sum of the terms of a sequence (correct)
  • The difference of the terms of a sequence
  • The product of the terms of a sequence
  • The ratio of the terms of a sequence

What is the notation used to represent the sum of terms in a sequence?

  • Gamma notation
  • Pi notation
  • Delta notation
  • Sigma notation (correct)

What is the upper bound in the general form of sigma notation?

  • i
  • n (correct)
  • m
  • T_i

What is the sum of the first n terms of a sequence denoted as?

<p>S_n (D)</p>
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What type of series sums infinitely many terms of a sequence?

<p>Infinite series (A)</p>
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What is the index of summation in the general form of sigma notation?

<p>i (B)</p>
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What is the term of the sequence at index i in the general form of sigma notation?

<p>T_i (C)</p>
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What is the lower bound in the general form of sigma notation?

<p>m (D)</p>
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What is the main difference between a finite series and an infinite series?

<p>The number of terms being summed (B)</p>
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What does the summation symbol ∑ represent?

<p>The sum of terms in a sequence (C)</p>
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What is the purpose of using sigma notation?

<p>To simplify the representation of the sum of terms (B)</p>
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What is the general form of sigma notation used for?

<p>To represent the sum of terms in a sequence (A)</p>
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What is the relationship between a sequence and a series?

<p>A sequence is the source of a series (B)</p>
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What does $S_n$ denote in a finite series?

<p>The sum of the first n terms of a sequence (D)</p>
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What is the purpose of the index of summation in sigma notation?

<p>To keep track of the terms being summed (C)</p>
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What is the main advantage of using sigma notation?

<p>It simplifies the representation of the sum of terms (D)</p>
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What is the primary reason why sigma notation is used to represent the sum of terms in a sequence?

<p>To provide a concise way of representing the sum (A)</p>
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What is the key difference between the notation for a finite series and an infinite series?

<p>The number of terms being summed (B)</p>
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Which of the following is an example of a finite series?

<p>$\sum_{i=1}^5 i^2$ (A)</p>
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What is the purpose of the lower bound in the general form of sigma notation?

<p>To specify the starting index of the sequence (D)</p>
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Which of the following is an infinite series?

<p>$2 + 4 + 6 + \cdots$ (D)</p>
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What is the term of the sequence being summed in the general form of sigma notation?

<p>$T_i$ (B)</p>
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Why is sigma notation useful when working with series?

<p>It provides a concise way of representing the sum (D)</p>
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What is the relationship between a sequence and a series?

<p>A series is the sum of the terms of a sequence (B)</p>
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