Introduction to Series - Kuta Software LLC

[Pages:4]Kuta Software - Infinite Algebra 2

Introduction to Series

Rewrite each series as a sum.

5

1) (4m2 + 4)

m = 1

5

3) n

n = 1

6

5) (3a2 - 2)

a = 1

4

7) (5m2 + 4)

m = 1

6 m2 + 1

9) m=1 m

5

11) m(m + 2)

m = 0

Evaluate each series.

7

13) (40 - n2)

n = 1

Name___________________________________ Date________________ Period____

5

2) (30 - k2)

k = 1

6

4) (50 - m)

m = 1

5

6) (100 - m)

m = 1

9

8) (20 - a2)

a = 4

9

10) (100 - n)

n = 4

4

12) (100 - k)

k = 0

5

14) 3k

k = 1

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Worksheet by Kuta Software LLC

7

15) (500 - a)

a = 1

5

17) a

a = 0

6

19) k2

k = 1

Rewrite each series using sigma notation. 21) 1 + 2 + 3 + 4

7

16) (30 - k)

k = 1

4

18) 2k

k = 0

5

20) 3m

m = 1

22) 3 + 9 + 27 + 81 + 243

23) 3 + 9 + 27 + 81 25) 4 + 8 + 12 + 16

11111 27) 1 + + + + +

2 3 4 5 6

Critical thinking questions:

29) Are these equal? Why or why not?

50 1

70

1

and

x=1 x

x = 21 x - 20

24) 1 + 4 + 9 + 16 + 25

12345 26) + + + +

2 3 4 5 6

123456 28) + + + + +

2 3 4 5 6 7

30) Rewrite the following so that it starts at x = 0

10

x(x + 1)

x = 7

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Introduction to Series

Rewrite each series as a sum.

5

1) (4m2 + 4)

m = 1

8 + 20 + 40 + 68 + 104

5

3) n

n = 1

1 + 2 + 3 + 4 + 5

6

5) (3a2 - 2)

a = 1

1 + 10 + 25 + 46 + 73 + 106

4

7) (5m2 + 4)

m = 1

9 + 24 + 49 + 84

6 m2 + 1

9) m=1 m 5 10 17 26 37 2+ + + + + 23 4 5 6

5

11) m(m + 2)

m = 0

0 + 3 + 8 + 15 + 24 + 35

Evaluate each series.

7

13) (40 - n2)

n = 1

140

Name___________________________________ Date________________ Period____

5

2) (30 - k2)

k = 1

29 + 26 + 21 + 14 + 5

6

4) (50 - m)

m = 1

49 + 48 + 47 + 46 + 45 + 44

5

6) (100 - m)

m = 1

99 + 98 + 97 + 96 + 95

9

8) (20 - a2)

a = 4

4 + (-5) + (-16) + (-29) + (-44) + (-61)

9

10) (100 - n)

n = 4

96 + 95 + 94 + 93 + 92 + 91

4

12) (100 - k)

k = 0

100 + 99 + 98 + 97 + 96

5

14) 3k

k = 1

45

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Worksheet by Kuta Software LLC

7

15) (500 - a)

a = 1

3472

5

17) a

a = 0

15

6

19) k2

k = 1

91

Rewrite each series using sigma notation.

21) 1 + 2 + 3 + 4

4

n

n = 1

7

16) (30 - k)

k = 1

182

4

18) 2k

k = 0

20

5

20) 3m

m = 1

45

22) 3 + 9 + 27 + 81 + 243

5

3m

m = 1

23) 3 + 9 + 27 + 81

4

3n

n = 1

24) 1 + 4 + 9 + 16 + 25

5

k2

k = 1

25) 4 + 8 + 12 + 16

4

4k

k = 1

11111 27) 1 + + + + +

2 3 4 5 6

6 1

a=1 a

12345 26) + + + +

2 3 4 5 6

5 a

a=1 a + 1

123456 28) + + + + +

2 3 4 5 6 7

6 a

a=1 a + 1

Critical thinking questions:

29) Are these equal? Why or why not?

50 1

70

1

and

x=1 x

x = 21 x - 20

30) Rewrite the following so that it starts at x = 0

10

x(x + 1)

x = 7

111 Yes. Both are 1 + + + + ??? to 50 terms

2 3 4

3

(x + 7)(x + 8)

x = 0

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at

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