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 e^{x}. 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 t_{n} = 1/n^{k}
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/(n1)  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.
