Introduction to Series - Kuta Software LLC to Series... · Introduction to Series Date_____...
4
©l O2D0M122m lKGu0tPaz vSNoffetgwRaMrBeN xLcLbC1.3 2 mA7lold LrEiBgShct1sT LrweisJeHrZvQe8dx.7 B eMVa6dEee vwfiQtwh1 nIBntfLiXnaizt0eb rAxlLgGeKbErWaW 12f.J Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name___________________________________ Period____ Date________________ Introduction to Series Rewrite each series as a sum. 1) Σ m = 1 5 (4m 2 + 4) 2) Σ k = 1 5 (30 - k 2 ) 3) Σ n = 1 5 n 4) Σ m = 1 6 (50 - m) 5) Σ a = 1 6 (3a 2 - 2) 6) Σ m = 1 5 (100 - m) 7) Σ m = 1 4 (5m 2 + 4) 8) Σ a = 4 9 (20 - a 2 ) 9) Σ m = 1 6 m 2 + 1 m 10) Σ n = 4 9 (100 - n) 11) Σ m = 0 5 m(m + 2) 12) Σ k = 0 4 (100 - k) Evaluate each series. 13) Σ n = 1 7 (40 - n 2 ) 14) Σ k = 1 5 3k -1-
Transcript of Introduction to Series - Kuta Software LLC to Series... · Introduction to Series Date_____...
©l O2D0M122m lKGu0tPaz vSNoffetgwRaMrBeN xLcLbC1.3 2 mA7lold LrEiBgShct1sT LrweisJeHrZvQe8dx.7 B eMVa6dEee vwfiQtwh1 nIBntfLiXnaizt0eb rAxlLgGeKbErWaW 12f.J Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________Introduction to Series
Rewrite each series as a sum.
1) Σ
m = 1
5
(
4
m2 + 4) 2) Σ
k = 1
5
(
30 −
k2)
3) Σ
n = 1
5
n 4) Σ
m = 1
6
(
50 −
m)
5) Σ
a = 1
6
(
3
a2 − 2) 6) Σ
m = 1
5
(
100 −
m)
7) Σ
m = 1
4
(
5
m2 + 4) 8) Σ
a = 4
9
(
20 −
a2)
9) Σ
m = 1
6
m2 + 1
m10) Σ
n = 4
9
(
100 −
n)
11) Σ
m = 0
5
m(
m + 2) 12) Σ
k = 0
4
(
100 −
k)
Evaluate each series.
13) Σ
n = 1
7
(
40 −
n2) 14) Σ
k = 1
5
3
k
-1-
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15) Σ
a = 1
7
(
500 −
a) 16) Σ
k = 1
7
(
30 −
k)
17) Σ
a = 0
5
a 18) Σ
k = 0
4
2
k
19) Σ
k = 1
6
k2 20) Σ
m = 1
5
3
m
Rewrite each series using sigma notation.
21)
1 +
2 +
3 +
4 22)
3 +
9 +
27 +
81 +
243
23)
3 +
9 +
27 +
81 24)
1 +
4 +
9 +
16 +
25
25)
4 +
8 +
12 +
1626)
1
2 +
2
3 +
3
4 +
4
5 +
5
6
27)
1 +
1
2 +
1
3 +
1
4 +
1
5 +
1
628)
1
2 +
2
3 +
3
4 +
4
5 +
5
6 +
6
7
Critical thinking questions:
29) Are these equal? Why or why not?
Σ
x = 1
50
1
x and Σ
x = 21
70
1
x − 20
30) Rewrite the following so that it starts at
x = 0
Σ
x = 7
10
x(
x + 1)
-2-
©q U2r0F1u2X hKcuotjaO xSYoKf0tBwKakrWeM 0LGL8Cm.G y PANlkli 1rUiKguhEtTsd GrpeVsNeurFvcegdS.S S SMxaOdneU FwFi4trhg JI3ngf9ienpiWtNeT OALlHgeeAbVrvar A2G.B Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________Introduction to Series
Rewrite each series as a sum.
1) Σ
m = 1
5
(
4
m2 + 4)
8 +
20 +
40 +
68 +
104
2) Σ
k = 1
5
(
30 −
k2)
29 +
26 +
21 +
14 +
5
3) Σ
n = 1
5
n
1 +
2 +
3 +
4 +
5
4) Σ
m = 1
6
(
50 −
m)
49 +
48 +
47 +
46 +
45 +
44
5) Σ
a = 1
6
(
3
a2 − 2)
1 +
10 +
25 +
46 +
73 +
106
6) Σ
m = 1
5
(
100 −
m)
99 +
98 +
97 +
96 +
95
7) Σ
m = 1
4
(
5
m2 + 4)
9 +
24 +
49 +
84
8) Σ
a = 4
9
(
20 −
a2)
4 +
(−5) +
(−16) +
(−29) +
(−44) +
(−61)
9) Σ
m = 1
6
m2 + 1
m
2 +
5
2 +
10
3 +
17
4 +
26
5 +
37
6
10) Σ
n = 4
9
(
100 −
n)
96 +
95 +
94 +
93 +
92 +
91
11) Σ
m = 0
5
m(
m + 2)
0 +
3 +
8 +
15 +
24 +
35
12) Σ
k = 0
4
(
100 −
k)
100 +
99 +
98 +
97 +
96
Evaluate each series.
13) Σ
n = 1
7
(
40 −
n2)
140
14) Σ
k = 1
5
3
k
45
-1-
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15) Σ
a = 1
7
(
500 −
a)
3472
16) Σ
k = 1
7
(
30 −
k)
182
17) Σ
a = 0
5
a
15
18) Σ
k = 0
4
2
k
20
19) Σ
k = 1
6
k2
91
20) Σ
m = 1
5
3
m
45
Rewrite each series using sigma notation.
21)
1 +
2 +
3 +
4
Σ
n = 1
4
n
22)
3 +
9 +
27 +
81 +
243
Σ
m = 1
5
3
m
23)
3 +
9 +
27 +
81
Σ
n = 1
4
3
n
24)
1 +
4 +
9 +
16 +
25
Σ
k = 1
5
k2
25)
4 +
8 +
12 +
16
Σ
k = 1
4
4
k
26)
1
2 +
2
3 +
3
4 +
4
5 +
5
6
Σ
a = 1
5
a
a + 1
27)
1 +
1
2 +
1
3 +
1
4 +
1
5 +
1
6
Σ
a = 1
6
1
a
28)
1
2 +
2
3 +
3
4 +
4
5 +
5
6 +
6
7
Σ
a = 1
6
a
a + 1
Critical thinking questions:
29) Are these equal? Why or why not?
Σ
x = 1
50
1
x and Σ
x = 21
70
1
x − 20
Yes. Both are
1 +
1
2 +
1
3 +
1
4 + ·· · to 50 terms
30) Rewrite the following so that it starts at
x = 0
Σ
x = 7
10
x(
x + 1)
Σ
x = 0
3
(
x + 7)(
x + 8)
-2-
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