Sigma Notation

Algebra 2 · Axiom Academy

One compact symbol stands in for an entire sum — read its parts, unroll it into terms, and write your own. Every summation is built from four working parts. Take and read it from the inside out: an index , a lower limit , an upper limit , and a summand — the rule you apply to each value of the index. The counter. It steps through the whole numbers one at a time; any letter works — i , k , or n . Where the index starts. The very first term uses this value. Where the index stops — and this value is itself included. The rule you evaluate at each index value to produce that term. To expand a summation, let the index sweep from the lower limit to the upper limit. At each stop you evaluate the summand and add the result to a running total — exactly like a loop keeping a tally. The first n odd numbers always sum to n^2 . 3. Writing a Sum in Sigma Form Going the other way, start from a written-out sum, find the rule that produces each term, then read off where the index must start and stop. Four terms, so the index runs i=1 to 4 . You can now read a , unroll it into its terms, and fold a written-out sum back into summation notation. Scroll up to revisit any step.

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