Week 4: Sigma Notation and its properties

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Week 4: Sigma Notation and its properties www.hndit.com Statistics for IT Week 4: Sigma Notation and its properties

Learning Outcome At the end of the module the student will be able to www.hndit.com Learning Outcome At the end of the module the student will be able to expand a sum given in sigma notation into an explicit sum; write an explicit sum in sigma notation where there is an obvious pattern to the individual terms; use rules to manipulate sums expressed in sigma notation.

www.hndit.com Sigma notation Sigma notation is a method used to write out a long sum in a concise way. For example, we often wish to sum a number of terms such as 1 + 2 + 3 + 4 + 5 or 1 + 4 + 9 + 16 + 25 + 36 where there is an obvious pattern to the numbers involved.

www.hndit.com Sigma notation… More generally, if we take a sequence of numbers u1, u2, u3, . . . , un then we can write the sum of these numbers as u1 + u2 + u3 + . . . + un . A shorter way of writing this is to let ur represent the general term of the sequence and put 𝑟=1 𝑛 𝑢 𝑛

www.hndit.com Some examples

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Writing a long sum in sigma notation www.hndit.com Writing a long sum in sigma notation Suppose that we are given a long sum and we want to express it in sigma notation. How should we do this? Let us take the two sums we started with. If we want to write the sum 1+2+3+4+5 and 1 + 4 + 9 + 16 + 25 + 36

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Rules for use with sigma notation www.hndit.com Rules for use with sigma notation There are a number of useful results that we can obtain when we use sigma notation. For example, suppose we had a sum of constant terms

www.hndit.com Rules….

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If we have any function g(k) of k, then we can write www.hndit.com If we have any function g(k) of k, then we can write Where a is a constant

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Further Worked Examples www.hndit.com Further Worked Examples

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www.hndit.com Thank You!