Sigma and the Binomial Theorem

Sigma and the Binomial Theorem

Pre-Calc: Lessons 12-5 and 12-6

12-5:

Sigma notation

Greek letter that represents a sum in mathematics. It is a concise way of representing a series.

Open Ended

Express in sigma notation:

2 + 4 + 10 + 28

Express using sigma notation:

 $\frac{2}{3}+\frac{4}{5}+\frac{8}{7}+\frac{16}{9}+.\ .\ .\ .$  

12-6:

The Binomial Theorem

Pascal's Triangle!

The secret to expanding binomials!

Expand (x - 2)³

1x³(-2)⁰ + 3x²(-2)¹ + 3x¹(-2)² + 1x⁰(-2)³

1x³ + 3x²(-2) + 3x¹(4) + 1x⁰(-8)

x³ - 6x² + 12x - 8

Multiple Choice

Expand

 $\left(3n+1\right)^4$  

•  $81n^4+108n^3+54n^2+12n+1$  

•  $81n^4-27n^3+9n^2-3n+1$  

•  $12n^4+9n^3+6n^2+3n+1$  

•  $81n^4+27n^3+9n^2+3n+1$  

Find the 6th term of

(x - y)⁷