1. ALGEBRA II H/G @ INTRODUCTION TO SERIES

2. SERIES : The sum of part (partial) or all of the terms of a sequence. The sequence 3, 8, 13, 18 can be written as the series 3 + 8 + 13 + 18. ∑ is the Greek letter sigma which means summation. 2 k = 2 1 + 2 2 + 2 3 + 2 4 + 2 5 is called sigma notation.

3. 1) What does SOLUTION : 3 1 + 3 2 + 3 3 + 3 4 + 3 5 2) What does SOLUTION : t 1 + t 2 + t 3 + t 4 + … + t n

4. 3) Evaluate. SOLUTION : = (2 3 1 ) + (2 3 2 ) + (2 3 3 ) + (2 3 4 ) = 6 + 18 + 54 + 162 = 240

5. 4) Evaluate. SOLUTION : = (-1) 0 [3(0) – 2] + (-1) 1 [3(1) – 2] + (-1) 2 [3(2) – 2] + (-1) 3 [3(3) – 2] + (-1) 4 [3(4) – 2] + (-1) 5 [3(5) – 2] = -2 + -1 + 4 + -7 + 10 + -13 = -9

6. Write using sigma notation. 5) S 30 = 1 + 8 + 27 + 64 + 125 + … SOLUTION : Hey, those numbers are all cubes.

7. 6) S 50 = 3 + 6 + 12+ 24 + 48 + … SOLUTION : Hmmm, the numbers are all multiple of 3, so let’s factor out a 3. 3(1 + 2 + 4 + 8 + 16 + …) Holy cow, look at the numbers in the (), they are all powers of 2. OR

8. WEB LINKS http://www.math.montana.edu/frankw/ ccp/general/sigma/learn.htm http://quiz.econ.usyd.edu.au/mathqui z/sigma/index.php