Tags » Sequences And Series

Geometric Series – Far Out

One of the great things – at least I like it – about Taylor series is that they are unique. There is only one Taylor series for any function centered at a given point, What that means is that any way you get it, it’s right. 324 more words

Power Series

Graphing Taylor Polynomials

The seventh in the Graphing Calculator / Technology series

Here are some hints for graphing Taylor polynomials using technology. (The illustrations are made using a TI-8x calculator. 444 more words

Power Series

Everyday Series

Our BC friends will soon be starting to teach series. Today, to emphasize that series are all around us, I would like to discuss series that we see every day: numbers. 762 more words

Sequences And Series

A Bonus Question on Convergent Series

Occasionally when teaching the sequences and series material in second-semester calculus I’ve included the following question as a bonus:

Question: Suppose  is absolutely convergent.  Does that imply anything about the convergence of ? 94 more words

Sequences And Series

Alternating Sum of the Reciprocals of the Central Binomial Coefficients

In the last post we proved the generating function for the reciprocals of the central binomial coefficients:

In this post we’re going to use this generating function to find the alternating sum of the reciprocals of the central binomial coefficients.   127 more words

Binomial Coefficients

Generating Function for the Reciprocals of the Central Binomial Coefficients

In this post we generalize the result from the last post to find the generating function for the reciprocals of the central binomial coefficients.  As we did with that one, we start with the beta integral expression for : 212 more words

Binomial Coefficients

Sum of the Reciprocals of the Central Binomial Coefficients

In this post we prove the formula for the sum of the reciprocals of the central binomial coefficients :

(Of course, the sum of the central binomial coefficients themselves does not converge.) 108 more words

Binomial Coefficients