Sigma Notation Of A Series - Varsity Tutors

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Sigma Notation of a Series

Study Guide

Key Definition

Sigma notation uses the symbol $\Sigma$ to denote the sum of a sequence of numbers.

Important Notes

  • The symbol $\Sigma$ is used to represent summation.
  • The expression after $\Sigma$ indicates what is being summed.
  • Limits on the top and bottom of $\Sigma$ show the range of summation.
  • Sigma notation provides a compact way to represent series.

Mathematical Notation

$\Sigma$ means summation$+$ represents additionRemember to use proper notation when solving problems

Why It Works

By encapsulating repeated addition in one symbol, sigma notation makes series compact and clear.

Remember

Focus on correctly identifying the index and limits when using $\Sigma$.

Quick Reference

Basic Sigma Notation:$\Sigma_{i=1}^{n} a_i$

Understanding Sigma Notation of a Series

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

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Beginner Explanation

Sigma notation uses $\Sigma$ to represent the sum of series in a concise way.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What does $\Sigma_{i=1}^{4} i$ equal?

A$10$B$15$C$20$D$25$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

A teenager starts with $3 of pocket money in the first week and receives $1 more each subsequent week for 5 weeks. Represent the total amount received using $\Sigma$ notation and calculate the total.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

If the sum of the first $n$ odd numbers is given by $\Sigma_{i=1}^{n} (2i-1)$, find $n$ when the sum is 49.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

What does $\Sigma_{k=1}^{n} (3k - 2)$ equal when $n = 5$?

A$35$B$40$C$45$D$50$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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