Tags » 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

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.   97 more words

Sequences And Series

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
Calculator

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.   711 more words

Sequences And Series

Calculating SECA Offsets for Clergy

Recently my pastor posed a problem to me: How to calculate his SECA offset?  The answer can be found using algebra or using infinite series.  (For the non-math inclined, skip to the bottom of this post for an answer.) 642 more words

Sequences And Series