## Mathematics 210 - Spring term 2003 - sixth assignment

This assignment requires you to submit several spreadsheets concerned with series and one with decimal expansions of fractions. It is due Monday, March 10. I repeat the instructions from the first lab:
• Question 1. Use the spreadsheet to build a template that lays out the series for ex. I.e. whenever x is placed in a0 the terms of the series and its partial sums will appear in columns b and c (index n in a). Put these columns in bar graphs, too. Then in separate sheets calculate e, e10, e20, e-20 as accurately as possible. Be very careful in telling how accurate the value of e-20 is.

Save these sheets as m210.6.1a.ms,m210.6.1b.ms, m210.6.1c.ms, and m210.1d.4.ms.

• Question 2. Lay out about 20 terms and partial sums for the series 1/n ln(n) and 1/n (ln(n))2 in one sheet. Make a bar graph comparing the terms of the two series.

The first series diverges. How many terms would it take to exceed 100?

The second converges. How many terms are necessary to obtain 2 significant figures? Indicate answers clearly on the sheet.

Save this sheet as m210.6.2.ms.

• Question 3. Make up a template spreadsheet that does this: when you put p into cell a0 and q into b0 (where you may assume p/q < 10) it lays out in one clearly marked column the first hundred digits in the decimal expansion of p/q. Your calculations must be exact, i.e. not depend on the quotient p/q calculated by the computer, but only using arithmetic with small integers.

Save this sheet as m210.6.3.ms.

• Question 4. Make a sheet that computes terms and partial sums for the harmonic series with terms 1/n. In the last column, calculate values of

1 + 1/2 + 1/3 + ... + 1/(n-1) - ln(n) .

Plot these in a bar graph. These values converge slowly to a certain number. Find this number to 2 decimals.

Save this sheet as m210.6.4.ms.

That's it!

If you find these questions confusing, please write me.