Find the sum of the series 1 + 1 2 + 1 3 + 1 4 + 1 6 + 1 8 + 1 9 + 1 12 + ⋯ where the terms are the reciprocals of the positive integers whose only prime factors are 2s and 3s.
Find the sum of the series 1 + 1 2 + 1 3 + 1 4 + 1 6 + 1 8 + 1 9 + 1 12 + ⋯ where the terms are the reciprocals of the positive integers whose only prime factors are 2s and 3s.
Solution Summary: The author explains that the sum of the geometric series is 3. The terms are the reciprocals of positive integers whose prime factors are 2 S and 3 S.
2. [-/4 Points]
DETAILS
MY NOTES
SESSCALCET2 7.3.002.
Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a = 6 and b = 2.)
ASK YOUR TEACHER
0
y = a sin(bx²)
Sketch a typical approximating shell.
y
6
4
2
x
π/b
y
2
1
x
0.5
1.0
1.5
0.2
0.4
0.6
0.8
1.0
-2
-1
-4
The graph of f', the derivative of f, is shown in the graph below. If f(-9) = -5, what is the value of f(-1)?
y
87 19
6
LO
5
4
3
1
Graph of f'
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2
3
4 5
6
7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
564%
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