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Stitz-Zeager_College_Algebra_e-book

# 371 111 2226 111 22 026 111 22 156 111 22 156 rounding

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Unformatted text preview: a matrix A = [aij ]m×n and the j th column Cj of a matrix B = [bij ]n×r as n Ri · Cj = aik bkj k=1 9.2 Summation Notation 563 Again, the reader is encouraged to write out the sum and compare it to Deﬁnition 8.9. Our next example gives us practice with this new notation. Example 9.2.1. 1. Find the following sums. 4 (a) k=1 4 13 100k (b) n=0 5 n! 2 (c) n=1 (−1)n+1 (x − 1)n n 2. Write the following sums using summation notation. (a) 1 + 3 + 5 + . . . + 117 111 1 (b) 1 − + − + − . . . + 234 117 (c) 0.9 + 0.09 + 0.009 + . . . 0. 0 · · · 0 9 n − 1 zeros Solution. 1. (a) We substitute k = 1 into the formula 4 k=1 13 100k = 13 100k and add successive terms until we reach k = 4. 13 13 13 13 + + + 1001 1002 1003 1004 = 0.13 + 0.0013 + 0.000013 + 0.00000013 = 0.13131313 (b) Proceeding as in (a), we replace every occurrence of n with the values 0 through 4. We recall the factorials, n! as deﬁned in number Example 9.1.1, number 6 and get: 4 n=0 n! 2 0! 1! 2! 3! 4! +++= 2 2 2 2 2 1 1 2·1 3·2·1 4·...
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