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. 760 more words

## Tags » 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

#### 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

#### 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

#### 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

#### A Proof of Dobinski's Formula for Bell Numbers

*Dobinski’s formula* entails the following infinite series expression for the *n*th Bell number :

In this post we’ll work through a proof of Dobinski’s formula. 97 more words

#### calculator and arithmetic sequences

The 26th term of an arithmetic sequence is 85, and the 16th term is 55.

Find the first term and the common difference.

- Name u1 the first term and d the common difference… 55 more words