Mathematics 210 - Spring term 2005 - Second assignment

This assignment requires you to submit several spreadsheets concerned with infinite series, and one extra. It is due before class time Monday, January 24.
  • Go to the MathSheet home page and then to the new applet page. Open a running copy of the spreadsheet and return to this page.
  • Log in immediately: File/Log in. Your login id is your Mathematics Department login name, and your password is your student number. This allows you to save and load spreadsheet files. Save your work frequently. To put it in simpler terms, save your work frequently.
  • Question 1. Make up a spreadsheet that calculates the partial sums of the Taylor series for ex. In column a will go 0, 1, 2, ... . In column b will go the terms of the series, and in column c will go the partial sums of the series. In cell d0 will go x. This is a general format for setting up series calculations on the spreadsheet.

    Calculate the first 60 terms and sums. Make also a bar graph of the terms of the series. Answer carefully: How accurate is the most accurate value you can find with the series and the spreadsheet for x = 0, 1, 5, 10, 15, -1, -5, -10, -15? (Put your answer as a string somewhere visible.)

    Save one complete sheet for each value, as, etc.

  • Question 2. Use the spreadsheet to calculate the first 1000 terms and partial sums of the series with tn = 1/nk for k = 2, 3, 4. (I.e. one series for each value of k.) In each case, plot the terms in a bar graph and estimate how accurate is the final sum you get? Considering the bar graph, figure out for each k approximately how many terms of the series would be necessary to compute the infinite sum to 2, 4, 8, 16 decimal places? Explain (put your answer in a string.)

    Save these sheets as etc.

  • Question 3. Use the spreadsheet to compute 1 + 1/2 + 1/3 + 1/4 + ... + 1/(n-1) - log(n) for n = 1 to 100. Plot the partial sums in a bar graph and estimate the limit to 2 decimal places. How large would n have to be to get the answer accurately to 5 decimal places?

    Save this sheet as

  • Question 4. Lay out 0 ... 500 in column a. Then lay out n! in column b. What is the largest n for which the spreadfsheet calculates n! exactly? What is the largest for which it gives any value for it? Set up a spreadsheet cleverly to calculate 500! (answer in scientific notation).

    Save this sheet as

If you find these questions confusing, please write me.