1.3 Sigma Notation and Limits of Finite Sums-Pangyen Weng
Student: _____________________
Date: _____________________
Instructor: Pangyen Weng
Course: Calculus II
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Assignment: 1.3 Sigma Notation and
Limits of Finite Sums
1. Write the sum without sigma notation. Then evaluate the sum.
2
15k
k=1
k+4
Write the sum without sigma notation. Choose the correct answer below.
15 • 1
A.
1+4
+
15 • 2
2+4
+
15 • 3
3+4
15k
B.
2+4
15 • 2
C.
2+4
15 • 1
D.
1+4
+
15 • 2
2+4
The value of the sum is
(Simplify your answer.)
.
2. Write the sum without sigma notation. Then evaluate.
5
cos k
k=1
Write out the sum.
5
cos k =
k=1
Evaluate the sum.
5
cos k =
(Simplify your answer.)
k=1
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1.3 Sigma Notation and Limits of Finite Sums-Pangyen Weng
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3. Which of the following expresses 1 + 2 + 4 + 8 + 16 + 32 + 64 in sigma notation?
7
6
(a)
2
k−1
(b)
k=1
5
2
k
(c)
k=0
2
k+1
k= −1
Choose the correct answer below.
6
2
k
k=0
7
2
k−1
k=1
All of them
5
2
k+1
k= −1
4. Graph the function f(x) = x2 − 1 over the interval [0, 2]. Partition the interval into four subintervals of equal length. Then add
to your sketch the rectangles associated with the Riemann sum
4
k=1
f ck
xk , given that ck is the (a) left-hand
endpoint, (b) right-hand endpoint, (c) midpoint of the kth subinterval.
(a) Choose the correct graph below.
A.
B.
C.
D.
C.
D.
C.
D.
(b) Choose the correct graph below.
A.
B.
(c) Choose the correct graph below.
A.
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B.
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1.3 Sigma Notation and Limits of Finite Sums-Pangyen Weng
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5. Graph the function f(x) = cos2 x on the interval [ − , ], showing the addition of the rectangles associated with the Riemann
4
sum
f ck
xk given that ck is the left endpoint of the kth subinterval.
k=1
Choose the correct graph.
A.
3 of 4
B.
C.
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1.3 Sigma Notation and Limits of Finite Sums-Pangyen Weng
1.
D.
15 • 1
1+4
+
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15 • 2
2+4
8
2. cos (1 ) + cos (2 ) + cos (3 ) + cos (4 ) + cos (5 )
−1
3. All of them
4.
C.
B.
C.
5.
A.
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