## 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.
• Question 1. Calculate (1 + 1/n)n for n = 8 doubling up to n = 232, 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/n2 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/n3/2 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.