Checkpoint 3

1. Show that the size of the `n`th tail of the logarithmic power series with `x=-1/2` is less than `1/(2^ntext[(]n+1text[)])`.
2. Substitute `x=-1//2` in the logarithmic series and simplify to find an explicit expression for the power series whose `n`th tail is estimated in part (a).
3. Find an `n` for which the estimate in part (a) is less than 0.001.
4. Add up `n` terms of the series in part (b), where `n` is the number you identified in part (c).
5. What logarithm should be approximated to within 0.001 by your answer to part (d)? Use your computer or calculator to check that the answer in (d) is within 0.001 of the appropriate logarithm.
6. How big is the actual error in your answer to part (d)? How good was your estimate of the error in part (a)?