13-6

This week in advanced math we learned chapter 13. In 13-1 we learned geometric and arithmetic sequences. In Chapter 13-2 we learned Recursive Definitions. In chapter 13-3 We learned Arithmetic and Geometric Series and their sums. In chapter 13-4 we learned Limits of Infinite Sequences. In chapter 13-5 we learned Sums of Infinite series. And finally in 13-6 we learned Sigma Notation. The greek letter sigma is often used in mathematics to express a series or its sum in abbreviated form. The Sigma contains three parts. The summand, the limits of summation, and the index. The number to the right of the Sigma is the summand. The number on top of the Sigma is the limits of summation. The number on the bottom of the Sigma is the index. You can either be asked to expand the Sigma or evaluate the sigma. To expand you only plug the numbers were they need to go. To evaluate you solve the whole thing.

Ex.Evaluate k=1; summand = (k+4); ;limit of summation = 25

1+4=5+4=9+4=13+4=17+4=21+4=25

Ex. Expand k=1; summand (k^3); limits of summation = 15

1^2 + 2^2 + 3^2... 15^2