Stitz-Zeager_College_Algebra_e-book

Two angles either a pair of right angles or one acute

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Unformatted text preview: tal Greek letter sigma and is n= shorthand for ‘sum’. The index of summation tells us which term to start with and which term to end with. For example, using the sequence an = 2n − 1 for n ≥ 1, we can write the sum a3 + a4 + a5 + a6 as 6 (2n − 1) = (2(3) − 1) + (2(4) − 1) + (2(5) − 1) + (2(6) − 1) n=3 = 5 + 7 + 9 + 11 = 32 The index variable is considered a ‘dummy variable’ in the sense that it may be changed to any letter without affecting the value of the summation. For instance, 6 6 6 (2k − 1) = (2n − 1) = n=3 (2j − 1) j =3 k=3 One place you may encounter summation notation is in mathematical definitions. For example, summation notation allows us to define polynomials as functions of the form n ak xk f (x) = k=0 for real numbers ak , k = 0, 1, . . . n. The reader is invited to compare this with what is given in Definition 3.1. Summation notation is particularly useful when talking about matrix operations. For example, we can write the product of the ith row Ri of...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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