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# Class Note for MATH 115A with Professor Dawson at UA

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This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15
mation Math 1 1 5A Spring 2008 Dawson Definitions Summation notation is used to write a sum of multiple terms efficiently 6 22x1x1x2x3x4x5x6 The GreekZIetter capital sigma 2 is called the summation operator 0 Here the letter a is the index of summation which tells you the variable in the expression to sum over Definitions ixix1x2x3x4x5x6 Here the number 1 is the lower limit of summation and the number 6 is the UQQeF limit of summation Examples 4 1 2 13 23 33 43 i1 182764 2100 2 25301 132 133 134 135 1 3v13v23v33v4 36912 30 Properties Property 1 0 Example 11 n 11 Eat ibi 2 Eat izbi i1 i1 i1 3 Zk2k 121222323 k1 122438 20 3 3 Zk22k 123212223 k1 k1 6248 20 Properties Property 2 n n Erai r 2 all i1 i1 3 Example 25k515253 k1 51015 30 3 SZk5123 k1 Properties Property 3 Suppose 1Smltn H m H Eat zai Eat i1 i1 im1 Notice on the right hand side the first lower limit and the second upper limit match the limits on the left hand side Properties Re indexing n n6 Zai Zara i1 j1c 0 Notice that the upper and lower limits increase or decrease by the same amount while the index of summation decreases or increases by that amount Objectives Use summation notation to express a given sum 0 Use direct computation to evaluate a given sum Use Excel to evaluate a given sum 0 Use the properties of summation to evaluate a given sum

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