Which Convergence Test Should I Use? Part 1

One common question from students first learning about series is how to know which convergence test to use with a given series.  The first answer is: practice, practice, practice. The second answer is that there is often more than one convergence test that can be used with a given series. I will illustrate this point…

More on Power Series

Continuing with post on sequences and series New Series from Old 1 Rewriting using substitution New Series from Old 2 Finding series by differentiating and integrating New Series from Old 3  Rewriting rational expressions as geometric series Geometric Series – Far Out A look at doing a question the right way and the “wrong” way?…

Amortization

This is an example of how sequences and series are used in “real life.”  It could be used in a calculus class or an advanced math class. When you borrow money to buy a house or a car you are making a kind of loan called a mortgage. Paying off the loan is called amortizing…

New Series from Old 3

Rational Functions and a “mistake” A geometric series is one in which each term is found by multiplying the preceding term by the same number or expression. This number is called the common ratio, r. Geometric series converge if, and only if, . If a geometric series converges, then the sum of the (infinite number…

New Series from Old 2

Differentiating and integrating a known series can help you find other series. Since  we can find the series for cos(x) this way  Of course we could also have integrated the series for sin(x) to get the series for  –cos(x) and then changed the signs. In out next post we will find that   Recall that…