Section 8.3: Series & Sigma Notation

This section introduces series notation and the use of the sigma (Σ) symbol to represent sums of sequences.

Example 1: Writing a Series Using Sigma Notation

Write the sum 2 + 4 + 8 + 16 + 32 using sigma notation.

Step 1: Recognize the geometric sequence: \( a_1 = 2, r = 2 \)

Step 2: Use sigma notation: \( \sum_{n=0}^{4} 2 \cdot 2^n \)

Example 2: Sum of a Series Using Sigma Notation

Compute \( \sum_{n=1}^{5} 3n \).

Step 1: Expand the sum: 3(1) + 3(2) + 3(3) + 3(4) + 3(5) = 3 + 6 + 9 + 12 + 15

Step 2: Add: 3 + 6 + 9 + 12 + 15 = 45

Practice Problems

  1. Write 5 + 10 + 20 + 40 + 80 using sigma notation
  2. Compute \( \sum_{n=1}^{6} 2n \)
  3. Express 1 + 4 + 9 + 16 + 25 using sigma notation
  4. Find the sum \( \sum_{n=1}^{5} (3n+2) \)
  5. Write the first 5 terms of \( 2^n \) in sigma notation
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