Here, that expression is just the index variable. The expression to the right of sigma describes or represents each addend, in terms of the index variable i.Here, the largest value i will take on is 10. The upper limit of summation indicates the largest value the index will take on.Unless indicated otherwise, we increase this value by 1 until we reach the upper limit of summation. Here, the smallest value i will take is 1. The lower limit of summation indicates the smallest value the index will take on.The dummy variable will usually show up one or more times in the expression to the right of the Greek letter sigma. The index of summation, here the letter i, is a dummy variable whose value will change as the addends of the sum change.The Greek letter sigma is closely associated with the word "sum." The letter sigma is a signal that summation notation is being used.The annotated symbolism shown below identifies important elementsused in summation notation (also called sigma notation). For instance, here is the summationnotation to represent the sum of the first 10 positive integers, thefirst sum described on this page. Summation notation provides for us a compact way to represent theaddends in sums such as these. See whether you candetect and describe the addend patterns in the following sums. The smallest addend is 2, each successive addend is 4 larger thanthe previous, and the largest addend is 18. The smallest addend is 1, each successive addend is one largerthan the one before it, and the largest addend is 10. In this content note we discuss and illustrate compact mathematical notation to express certain types of sums and products.Īt times when we add, there is a pattern by which we can expressthe addends. MAT 305: Combinatorics Topics for K-8 Teachers Illinois State University Mathematics Department
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