Explanation

A geometric series can also be written using summation notation:

Σ (from k = 0 to n−1) of arᵏ = a + ar + ar² + … + arⁿ⁻¹

• k = term index

• a = first term

• r = common ratio

• n = number of terms

Example:
Σ (k=0 to 3) of 2(3)ᵏ = 2(3⁰ + 3¹ + 3² + 3³) = 2(1 + 3 + 9 + 27) = 2×40 = 80

Quiz

1. Write 1 + 3 + 9 + 27 in summation notation.

2. What does k represent?

3. Use formula to sum Σ (k=0 to 4) of 2(2)ᵏ.

4. Can summation start at k = 1?

5. Is this series geometric?

Answer Key

1. Σ (k=0 to 3) of 3ᵏ

2. Term index

3. S₅ = 2(1−2⁵)/(1−2) = 62

4. Yes

5. Yes