Test 3 Review
1) Convince me that the convergence of a series does not depend upon the first few terms of a series.
2) Know how to read a simple theorem, for example:
If the series converges, then the sequence †converges to 0.
This theorem is of the form, If A, then B,† where A is the hypothesis, or conditions
to be met, and B is the conclusion.
The converse of a theorem is found by reading it backwards:† If B, then A.
The converse is not always true. Here, the converse is
If the sequence converges to 0, then the series converges.
This is not true since the sequence †converges to 0, but the series diverges.
Sometimes the contrapositive of a theorem is useful.† This is found by writing
If not B, then not A.
In the above theorem, the contrapositive results in the useful theorem:
If the sequence does not converge to 0, then the series diverges.†
This is the Nth term test for divergence.
3) I will not put a host of problems on the test and ask you
to test for convergence.† Rather,
I will tell you which test to use (you will need to know† how to use all of
the tests) and I will test you on your understanding of the results.
4) Be able to approximate a function using a Taylor or Maclaurin polynomial.† I think
I will give you Taylorís theorem so you will not have to memorize it.
5) Know what a sequence of partial sums is, and what purpose it serves.† I will give
you one for which the general term is easy to find.† Page 559 example 1a would be
worth your time.†
Thatís all folks!