Sigma Notation

Explore index and bounds, expanding a sum, properties of sums.

Lesson 3 of 53 parts Practice Flashcards

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Index and Bounds

Objective: Explain index and bounds and use it to solve or interpret a problem.

Sigma notation Σ uses an index and lower/upper bounds to specify the terms included in a sum; check whether bounds are inclusive. Exactly n indices.

Worked examples

Try itSigma Notation — practice 1.1: Evaluate Σ from k=1 to 5 of 2.Show answer

Step 1: There are 5 terms. Step 2: Each term equals 2. Step 3: Add them to get 10.

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Index and Bounds

Objective: Explain index and bounds and use it to solve or interpret a problem.

Sigma notation Σ uses an index and lower/upper bounds to specify the terms included in a sum; check whether bounds are inclusive. Exactly n indices.

Worked examples

Try itSigma Notation — practice 1.1: Evaluate Σ from k=1 to 5 of 2.Show answer

Step 1: There are 5 terms. Step 2: Each term equals 2. Step 3: Add them to get 10.

Expanding a Sum

Objective: Explain expanding a sum and use it to solve or interpret a problem.

Write the first few indexed terms before applying a formula; this prevents off-by-one errors and clarifies patterns. It reveals the index-to-term rule and bound count.

Worked examples

Try itSigma Notation — practice 2.1: Find the sum of 8 terms: 3, 7, ... with common difference 4.Show answer

Step 1: Use Sₙ=n[2a₁+(n−1)d]/2. Step 2: Substitute n=8, a₁=3, d=4. Step 3: The sum is 136.

Properties of Sums

Objective: Explain properties of sums and use it to solve or interpret a problem.

A constant can factor outside a sum and separate sums can combine over equal bounds; changing bounds requires care. No, the included terms may differ.

Worked examples

Try itSigma Notation — practice 3.1: Evaluate Σ from k=1 to 11 of 2.Show answer

Step 1: There are 11 terms. Step 2: Each term equals 2. Step 3: Add them to get 22.

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