04/19/23 Perkins

AP Calculus AB

Day 4Section 4.2

Notation

Examples

1

n

ii

a

6

1i

i

52

3j

j

start at 1

finish at n

index or counter

means summation

“sigma”

1 2 3 na a a a

1 2 3 4 5 6

2 2 23 4 5

21

To evaluate with calculator:

( (expression,variable,start,finsum seq ish))LIST menu:

50

( (x,x,sum seq 1,6))

2s ( (x ,x,3um seq ,5))

Properties

Shortcuts

1

n

i

ki

1

.n

i

a c

1

n

i ii

a b

1

.n

i

b i

2

1

.n

i

c i 3

1

.n

i

d i

1

n

i

k i

1 1

n n

i ii i

a b

cn 1

2

n n

1 2 1

6

n n n

22 1

4

n n

1. Evaluate 21

2n

i

i

n

if 10n

21

12

n

i

in

21 1

12

n n

i i

in

2

112

2

n nn

n

1 2

2

n

n n

5

2

n

n

10 5

2 10

3

4

2. Write in notation.

22 2 231 2 44 4 4 41 1 1 1

4

20

13. Evaluate

1k k

4

2

41

1 i

i

2 2 2 2 2

1 1 1 1 1

0 1 1 1 2 1 3 1 4 1

Shortcuts don’t work!

1 1 1 1 1

2 5 10 17

158

85 2sum( (1/ x 1 ,x,e )s q 0,4)

20

2

1

4. Evaluate 1i

i

(use shortcuts)

202

1

2 1i

i i

20 20 20

2

1 1 1

2 1i i i

i i

20 20 1 2 20 1 20 20 12 1 20

6 2

20 21 41

20 21 206

2870 420 20

2470 2( ( 1 ,xsum se ,1,q 20))x

Perkins

AP Calculus AB

Day 4Section 4.2

Notation

Examples

1

n

ii

a

6

1i

i

52

3j

j

Properties

Shortcuts

1

n

i

ki

1

.n

i

a c

1

n

i ii

a b

1

.n

i

b i

2

1

.n

i

c i 3

1

.n

i

d i

1. Evaluate 21

2n

i

i

n

if 10n

2. Write in notation.

22 2 231 2 44 4 4 41 1 1 1

4

20

13. Evaluate

1k k

20

2

1

4. Evaluate 1i

i

(use shortcuts)