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| 1. | a. | (2 • 1 - 3) + (2 • 2
- 3) + ... + (2 • 8 - 3) = -1 + 1 + 3 + ... + 13 = 48 |
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| b. | (02 + 0) +
(12 + 1) + (22 + 2) + ... + (102 + 10) = 0 + 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 + 90 + 110 = 440 |
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| c. | (1/2
+ 2 - 1) + (1/3
+ 3 - 1) + (1/4
+ 4 - 1) + (1/5
+ 5 - 1) + (1/6
+ 6 - 1) = 11/2 + 21/3 + 31/4 + 41/5 + 51/6 = 16,45 |
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| d | (-5 • (2--5)) +
(-4•(2--4)) + (-3 • (2--3)) + (-2 • (2--2)) + (-1 • (2--1)) + (0 •
(2--0)) = -5 • 7 + -4 • 6 + -3 • 5 + -2 • 4 + -1 • 3 + 0 • 2 = -35 - 24 - 15 - 8 - 3 - 0 = -85 |
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| e. | (-100 + 1) + (-99 + 1) + ... +
(100 + 1) = -99 + -98 + -97 + ... + 101 = -99 + -98 + ..... + 98 + 99 + 100 + 101 = 201 |
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| f. | (-1)5 + (-1)6
+ ... + (-1)12 = -1 + 1 - 1 + 1 - ... - 1 + 1 = 0 |
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| g. | 2/3
+ 3/4
+ 4/5
+ 5/6
+ 6/7
+ 7/8 = 1339/280 |
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| h. | 4 + 4 + .... + 4 (601
stuks) = 4 • 601 = 2404 |
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| 2. | n = 1:
(2 - 1) = 1 = 12 n = 2: (2 - 1) + (4 - 1) = 1 + 3 = 4 = 22 n = 3: (2 - 1) + (4 - 1) + (6 - 1) = 9 = 32 het lijkt inderdaad te kloppen. |
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| 3. |
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| Samen geeft dat 1 + 5 + 14 + 30 = 50 | |||||
| 4. | a. | √1 + √2 + √3 + √4 + √5 ≈ 8,38 | |||
| b. | 2f(0) + 2f(1) + 2f(2)
+ ... + 2f(10) = 2 • -4 + 2 • -1 + 2 • 2 + ... + 2 • 26 = 242 |
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| c. | f(0) + f(2) + f(4)
+ ... + f(20) = -4 + 2 + 8 + 14 + 20 + ... + 56 = 286 |
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| d. | 1/(3-1) +
1/(4-1) + 1/(5-1) + 1/(6-1)
+ 1/(7-1) + 1/(8-1) = 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 = 223/140 |
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| e. | f(x0) +
f(x1) + f(x2) + f(x3)
+ f(x4) + f(x5) = f(0) + f(0,1) + f(0,2) + f(0,3) + f(0,4) + f(0,5) = (1 + 0) + (1 + 0,1) + (1 + 0,2) + (1 + 0,3) + (1 + 0,4) + (1 + 0,5) = 7,5 |
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| f. | f(x0) +
f(x1) + f(x2) + f(x3) = f(1) + f(3) + f(5) + f(7) = 12 + 32 + 52 + 72 = 84 |
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| 5. | a. |
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| b. |
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| c. |
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| d. |
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© h.hofstede (h.hofstede@hogeland.nl) |
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