|
|
You are here: Home / Category Index / Sequences And Series / Telescoping Series (scarification!)
|
Telescoping Series (scarification!) - By Aidan Lynch
How to use this applet:
How To Use The Applet
This applet is extremely simple to use. It will take you step by step through how to solve a
telescoping series problem. All you have to do is click on the "Next" or "Previous" buttons.
These will take you forward and backwards through the show. Each slide explains in detail
what is involved in each step. After every five slides, there is an opportunity to run an
animation. This animation will animate the idea put forward in the previous five slides. All
you have to do to run the animation is click on the "Run Animation" button, every fifth
slide. Alternatively, you can just hit "Next" as usual and the animation will run anyway!
Notes on the maths used in the applet:
There are three main parts to solving telescoping series:
- 1. Splitting the Fraction
- 2. Scarification
- 3. Getting the Sum to n terms (Sn) of the series
SPLITTING THE FRACTION
Splitting the fraction is a simple process. You multiply both sides by the denominator of
the combined fraction. This is explained in detail in the applet itself.
SCARIFICATION
"Scarification" is a process which describes how the individual terms cancel out with each
other. As you will see in the applet, the individual terms line up over each other. Then
they "cancel out" diagonally. This looks like several "scars" going across the page when the
terms are cancelled out - hence the name "scarification"! To achieve the cancelling out
effect, it is important to notice that the second half of one term is equal in magnitude but
opposite in sign to the first half of the following term. This allows them to cancel out
with each other (don't worry if it doesn't make too much sense just reading this - the
applet will explain it better).
CALCULATING Sn
This, the third and final, part of the problem involves adding up each of the terms to
determine Sn. It is slightly intuitive in that you should learn to spot that all
the terms cancel out with each other, except for the first and last terms. This will become
apparent in the animation part of the applet.
Other useful information: Feel free to check out the other Sequences and Series applets on this website for further
assistance regarding Sequences and Series.
|
|
