## 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.
• 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 m210.2.1a.ms, 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 m210.2.2a.ms 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 m210.2.3.ms.

• 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 m210.2.4.ms.

If you find these questions confusing, please write me.