Laurent Series Representations

Solution 18 (b).

Solutions.

Sequence (i).   For the sequence    we have

                     [Graphics:../Images/LaurentSeriesModHome_gr_725.gif]

Therefore,      is valid for  .

Sequence (ii).   For the sequence    we have

                     [Graphics:../Images/LaurentSeriesModHome_gr_729.gif]

Therefore,      is valid for  .

Sequence (iii).   For the sequence    we have

                     [Graphics:../Images/LaurentSeriesModHome_gr_733.gif]

Therefore,      is valid for  .

Sequence (iv).   For the sequence    we have

                     [Graphics:../Images/LaurentSeriesModHome_gr_737.gif]

Therefore,      is valid for  .

We are done.

Aside. We can let Mathematica double check our work.

This solution is complements of the authors.