Eva Curry Acadia University, NS - Math 1023

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.

s_n = 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.

f1 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 = π²/90

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

This Mathematics has been solved by our PHD Experts at My Uni Paper.