Mathematics 210  Spring term 2005  Sixth assignment
This assignment requires you to submit spreadsheets concerned
with Richardson extrapolation.
It is due before class time Monday, March 7.

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.
Calculate (1 + 1/n)^{n} for
n = 8 doubling up to n = 2^{32}, and use Richardson
extrapolation three times to get chains of accelerated estimates.
Which of all the estimates you get is most accurate?
Which is least? Explain in a comment.
Save as m210.6.1.ms.

Question 2.
Display in the first three columns the sum of the series
1/n^{2} up to 4096 terms.
Comment on how accurate the final estimate is, using the integral
comparison. How many terms would you need to get an estimate correct to 6
decimals? 10?
Use Richardson extrapolation applied to the sum of N terms for
N = 128 up to 4096 terms to get accelerated estimates.
Do it again a second time. And a third.
How accurate is your final estimate?
Save as m210.6.2.ms.

Question 3.
Display in the first three columns the sum of the series
1/n^{3/2} up to 4096 terms.
Comment on how accurate the final estimate is, using the integral
comparison. How many terms would you need to get an estimate correct to 6
decimals? 10?
Use Richardson extrapolation applied to the sum of N terms for
N = 128 up to 4096 terms to get accelerated estimates.
Do it again a second time. And a third.
How accurate is your final estimate?
Save as m210.6.3.ms.

Question 4.
Use Richardson extrapolation to estimate the limit
of the 1 + 1/2 + 1/3 + ... + 1/n  ln(n)
as n goes to infinity with 10 decimal accuracy.
Save as m210.6.4.ms.
If you find these questions confusing, please
write me.
