Definition: Sigma notation uses the Greek letter sigma to write a sum compactly, showing a formula, an index variable, and the first and last values of that index.
How do you read it?
The symbol Σ means “add up.” Below it sits the index and its starting value, above it the ending value, and to the right the formula to evaluate at every index.
The expression Σ (k = 1 to 5) of (3k – 2) means: plug in k = 1, 2, 3, 4, 5 and add the results.
How do you evaluate one?
Worked example: the terms are 3(1) – 2 = 1, 4, 7, 10, 13. Their sum is 1 + 4 + 7 + 10 + 13 = 35.
Because the terms form an arithmetic sequence, you can also use (number of terms) times (first + last) divided by 2: 5 times 14 divided by 2 = 35.
What mistakes occur?
Students miscount the number of terms, especially when the index starts at 0 or 3. From k = 3 to k = 9 there are 7 terms, not 6. Mathbot counts with end minus start plus one.