In This Chapter
Sequences involving polynomials and formulas for their sums
Describing special patterns and adding them
Sequences for e and sin x
A sequence is a list of terms that has a formula or pattern for determining the numbers to come. A series is the sum of the terms in a sequence. Chapter 15 explains several types of sequences and series. In this chapter, I give you the power to add up lists of numbers — sometimes a huge number of numbers. Many sequences of numbers are used in financial and scientific formulas, and being able to add them up is essential. This chapter doesn’t contain all the sum formulas possible, but the formulas here are the most common.
In Chapter 17, I tell you about basic graphs you can change through translations. The formulas in this chapter can be changed, too, but you’ll have to wait until you get to a more advanced math course to get the opportunity. For now, just enjoy.
The positive integers are 1, 2, 3, 4, 5, … , going on forever. Find the sum of the first n terms of this sequence using this formula:
So, if you want the sum of the first 100 integers, you do the ...