Assignment Task
Write up the solutions to the indicated problems. Write solutions to written questions 1-4 in the level of detail required for tests. Write a full solution to written question Following the criteria on the Written Assignment Rubric. Submit your solutions, with a signed copy of the Assignment Marking Rubric as the first page, in class on Wednesday, March 15th
Questions
1. Calculate the sum of the series Σ n = 1 anwhose partial sums are given.
sn = 8 − 7(0.6) n
2. Use a geometric series or the Divergence Test to determine the convergence or divergence of the series.
Σ n = 0 2n + 1 9n + 7
Converges
Diverges
3. Consider the following.
0.03
4. Write the repeating decimal as a geometric series.
Σ n = 0
5. Write the sum of the series as the ratio of two integers.
6. Watch the video to find the formula for partial sums of a geometric series. Then use this formula to answer the.
7. A manufacturer producing a new product, estimates the annual sales to be 9,800 units. Each year, 8% of the units that have been sold will become inoperative. So, 9,800 units will be in use after 1 year, [9,800 + 0.92(9,800)] units will be in use after 2 years, and so on. How many units will be in use after n years?
8. Tutorial Exercise Use the Integral Test to determine whether the series is convergent or divergent.
Σ n =15/15
9. Use the Integral Test to determine whether the series is convergent or divergent.
Σ n = n4e – n5
10. Evaluate the following integral.
f
1 X4e – x5 dx
11. Consider the following function.
f(x) = 8 cos (πx) x
12. What conclusions can be made about the series Σ n = 8 Cos(πn)n and the Integral Test?
13. The Integral Test can be used to determine whether the series is convergent since the function is positive and decreasing on [1, ∞).
14. The Integral Test can be used to determine whether the series is convergent since the function is not positive and not decreasing on [1, ∞).
15. The Integral Test can be used to determine whether the series is convergent since it does not matter if the function is positive or decreasing on [1, ∞).
16. The Integral Test cannot be used to determine whether the series is convergent since the function is not positive and not decreasing on [1, ∞).
17. There is not enough information to determine whether or not the Integral Test can be used or not
18. Find the sum of the convergent series.
Σ n = {(3/4)
n –
(n + 1)(n + 2)}
19. Euler found the sum of the p-series with p = 4:
(4) = Σ n = 1/n4 = π
2/90
20. Use Euler’s result to find the sum of the series.
Σ n = (3/n)4
K = 6 (k-3)1/4
21. Test for convergence or divergence, using one of the tests listed below.
Σ n = 7 n3 + 216
converges
Diverges
22. Identify which test you used.
Divergence Test
Geometric Series Test
p-Series Test
Telescoping Series Test
Integral Test
Comparison Test
23. Use the Integral Test or a p-series to determine the convergence or divergence of the series.
Σ n = ln(n) n8
Converges
Diverges
