Aim: How do we use summation notation? + 2 + 2

Lesson_39_Summation_Notation.notebook

May 14, 2014

Aim: How do we use summation notation? PAGE 981/2,4,7,12,13,14,17,27

Do Now: Find the sum of:

22 + 23 + 24

How can the sum be written using summation notation?

May 22­12:50 PM

In statistics, it is common to need the sum of a collection of data. The Greek capital letter sigma, written Σ, is the symbol used to indicate summation. 4

i

The sigma notation Σ 2 means find the sum of the 2i i=2 terms for every consecutive integer i, from i = 2 to i = 4. In this notation, i is called the index, and does not mean the imaginary unit for √-1 . 4

Example: Evaluate

i Σ 2

i=2

Upper Limit

4

2 Σ i=2

i

= 22 + 23 + 24 = 4 + 8 + 16 = 28 Lower Limit May 24­9:31 PM

1

Lesson_39_Summation_Notation.notebook

May 14, 2014

Examples: 5

1.

Σ k2 + 2

k=1

4

2.

Σ sin nπ

n=0

2

May 24­9:48 PM

4

3. If x0 = 1,  x1 = 6, x2 = ­2, and x3 = ­1, find x4 if

Σ xi = 12

i=0

4

4. The value of

Σ 6Cr

is: 1) 15

2)35

3)50

4)64

r=2

May 26­12:35 PM

2

Lesson_39_Summation_Notation.notebook

May 14, 2014

Pair Work 3

5

1.

Σ 4k

4.

Σ (k2+ 1) 7. 2

k=0

k=2

4

2.

Σ k=1

k k+1

4

3.

Σ k2 k=1

5.

k2

k=2

4

3

(Σ )

Σ (k3 + 1) k=2

4

8.

Σ

3(x + 1)

x=2

4

6. 1

3

Σx

2

x=1

9.

4

Σ

cos nπ

n=0

2

May 22­1:12 PM

3