This Applet Demonstrates Convergence Of An Infinite Series, Which Is A Sub Series Of The MacLaurin Series (or The Taylor Series)

In the applet, two trains are on the same track, their speeds and initial distance apart are specified by the user.  There is also a fly on one train.

This applet calculates the total distance the fly will travel (each trip getting smaller, creating an Infinite Series) before the trains collide.

To calculate the total distance travelled by the fly, this applet calculates the distances travelled by each train and the distance between them for every trip the fly makes from one train to another.

Then, using this remaining distance and the relative velocity of the train the fly started from, it calculated the time of the next trip.

This time is then used to calculate the distance of the fly's journey. Now we have a term of our Infinite Series.

Introduction

Explaination

Credits