University:
Missouri State University
Course:
MTH 137 | Precalculus 2
Academic year:

2022
Views:

397

Pages:

3
Author:

Heidy Larsen

Name: _______________________ Unit 5: Summation Notation (Sigma Notation) Sigma =  (Greek letter) used for sum of a sequence _________  _________ _________ Examples: 5 6  k  1  2  3  4  5  15  3k  3(2)  3(3)  3(4)  3(5)  3(6)  60 k 1 5 k 2 3 k 1 k 0  k 2  12  22  32  42  52  55  k 3  03  13  23  33  36 Properties of Sigma Notation n n n 1.  cak  c  ak k 1 k 1 3 Ex: 2.  (a k 1 k 3 k 1 k 1 k 1 2 k 1 k 1 3 3 3 k 1 k 1 k 1 n 2.  k  1  2  3  ...  n  k 1 k 1 n 3.  k 2  12  22  32  ...  n 2  k 1 n(n  1)( 2n  1) 6  n(n  1)  4.  k  1  2  3  ...  n    2  k 1 n 3 3 3 3 3 Calculator Shortcut sum(seq(expression, variable, lower,upper) 3 k 1 Special Summation Formulas 1.  c  nc 2  (k 3  k 2 )   k 3   k 2 (DIFFERENCE) Ex: n 3  (k  k )   k   k (SUM) Ex: k 1 n  bk )   a k   bk 3  4k  4  k n 2 n(n  1) 2 Name: _______________________ Examples: Write out the terms of the given expressions and then find each sum. 5 1.  4   (1) k  3  k 2 2.    k k 0 k 1 Write the following sums using sigma notation. 1 1 1 1 1     2  4  6  8  10  12  ...  44 4. 3 9 27 81 243 3. 1   2  1 5. f ( x1 )  f ( x2 )      f ( xn ) Using your properties and the summation formulas evaluate the following sum.  2k 50 6. 2   3k  4  k 1  k 10 7. 3   k2  k 2   k 20 8. 2   5k  k 11 Now, use your calculators to confirm your answer found above. ____________________ ___________________ ____________________ Name: _______________________ Unit 5 Worksheet 5 Write out the terms of the given expressions and then find each sum. 5 1. 5  3k  1 i   1 2i1 5. k 1 6 2. 3. 2i  2 1 i i 3 6 4.  1i  i  2 i 2i  1 4  i 1 5 i 1 2 6. 6  7. k 1 7   j  1 2  cos(k ) 8. k 1 j 2 Write the following sums using sigma notation. 1  2  3      98 9. 14. 10. 2  4  6      100 15. 11. 1  4  9  16  25  36 16. 1 1 1 1 12. 1         17. 2 3 4 50 3 3 3 3    13. 18. 5 25 125 625 Calculate each of the following if 10 19.  f (w1 )x  f (w2 )x      f (wn )x 1 8 -1   10 i 1 i 1 1 1 1   27 64 125  ai  40 and  bi  50 . 10 21.  3ai  2bi  22.  4ai  bi  2 i 1 10 20. a1  a2  a3      an b3  b4  b5      b22 f (c1 )  f (c2 )      f (cn ) 10 (2ai  bi ) i 1  k  sin    2  10  2bi  4 i 1 i 1 Using your properties and the summation formulas, evaluate the following sum. Then, verify the accuracy of your answer using your calculator shortcut.  3k 8 23. 2   7k  10  k 1 10 24.  8k  7k   2 k 2 5k k  4 25.  k 28. 2  2i  3 45 k 1 64 26.  2   k 40 27. k  17 2  k  3 k 1 n i 1  k2 

Summation Notation (Sigma Notation)

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