
Archives
 May 2017
 April 2017
 March 2017
 February 2017
 January 2017
 December 2016
 November 2016
 October 2016
 September 2016
 August 2016
 July 2016
 June 2016
 May 2016
 April 2016
 March 2016
 February 2016
 January 2016
 December 2015
 November 2015
 October 2015
 September 2015
 August 2015
 July 2015
 June 2015
 May 2015
 April 2015
 March 2015
 February 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 May 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011

Meta
Category Archives: sequences and series
A Bonus Question on Convergent Series
Occasionally when teaching the sequences and series material in secondsemester calculus I’ve included the following question as a bonus: Question: Suppose is absolutely convergent. Does that imply anything about the convergence of ? The answer is that converges. I’m going … Continue reading
Posted in calculus, sequences and series
6 Comments
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. … Continue reading
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.) We start with the beta integral, . Replacing n … Continue reading
Posted in binomial coefficients, sequences and series
1 Comment
A Proof of Dobinski’s Formula for Bell Numbers
Dobinski’s formula entails the following infinite series expression for the nth Bell number : In this post we’ll work through a proof of Dobinski’s formula. We’ll need four formulas: The Maclaurin series for : . The formula for converting normal powers to falling … Continue reading
Posted in Bell numbers, sequences and series, Stirling numbers
1 Comment
An Explicit Solution to the Fibonacci Recurrence
The Fibonacci sequence is a famous sequence of numbers that starts 1, 1, 2, 3, 5, 8, 13, 21, and continues forever. Each number in the sequence is the sum of the two previous numbers in the sequence. It’s easy to … Continue reading
Calculating SECA Offsets for Clergy
Update: Apparently you have to adjust your compensation by a factor of 0.9235 before calculating the selfemployment tax. See comments at end. Recently my pastor posed a problem to me: How to calculate his SECA offset? The answer can be found … Continue reading
Posted in applications, sequences and series
3 Comments