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Kuta Software - Infinite Algebra 2 Name_ Period Introduction to Series Date Rewrite each series as a sum. 1) E ( 4m2 + 4) 2 ) _ (30 - K2 ) 3 ) [ (5 4) (50-m) m = 5) [ (3a2 - 2) EAS + 18 + 1540+8 ($5 6) E (100 - m) 7) [ ( 5m 2 + 4 ) 8) _ (20 - a2 ) m = 1 a = 4 m' + 1 9) 10) E (100 -n) m = 1 m n = 4 CBS 11) [ m(m + 2 ) 12 ) _ (100 - k ) tenoflesup gobind fooling Evaluate each series. of aniwollof ord offwasl (OF Clon wilw 10 edW Plaupo seardi DIA 198 13 ) _ ( 40 - n ? ) 14) _ 3k 1= 1 OS - MESigma Notation Mini Lesson We use the Greek letter sigma ({ ) to simplify notation for the formula for the general term of a series. The expression: 14 E (4n - 3) n=1 Is read as: "the sum of 4n - 3 as n goes from 1 to 4. Therefor, E (4n - 3) = 1+5+9+ 13 = 28 n =1 Using Sigma Notation will not help to calculate a series any faster, but it is a more convenient way to write, it. Practice Compute the following. 5 a. E (8 - 6n) n= 1 4 b. [ 3 (2-1) n=1 8 2 (20 4 C. E (- 1)n+1 1 n=1 00 The sum of an infinite series is written as 1 n = 1 The above example would equal 1+ + + +... Describe the series below. (What does it represent?) 00 d. E n= 1 Vn15) _ (500 - a) 16) E (30 - k) 1= 1 17) a 18 ) E 2 k a =0 19 KEO 2 19) C K 2 20) _ 3m is p more son m = 1 Rewrite each series using sigma notation. 21) 1 +2+3+4 22) 3+9+27 +81+243 23) 3+9+27+81 24) 1 + 4+9+16+25 25) 4+8+12+16 W 26) WIN + + 27 ) 1 + 1 1 1 + + alur w IN 2 3 4 5 + 6 28 N / - + Critical thinking questions: 29) Are these equal? Why or why not? 30) Rewrite the following so that it starts at x = 0 1 and El X x =21 x - 20 [x(x+ 1) * = 7