Lecture 2 : Convergent & Bounded Sequences [ Section 2.1 : Need to consider sequences ]
2.1 Need to consider sequences :
The aim of this lecture is to introduce the concept of a sequence. Sequences arise naturally in various fields. Any iterative process gives rise to a sequence of observations. A sequence can be thought of as a list of objects written in a definite order.
2.1.1 Example (Finding the area of the unit circle) :
Greek mathematicians (400 B.C.) analyzed this problem by inscribing regular polygons inside the circle. If denotes
the area of the -sided polygon inscribed in the circle, then we get the sequences of numbers,,.....,. Click here to View the Interactive animation : Applet 1.3
2.1.2
Example (Zeno's paradox) :
A man standing in a room can not walk to the wall. In order to do so, he would have to go half the distance, then half the remaining distance, and then again half of what shall remains. This process can always be continued and can never be ended.
Click here to View the Interactive animation : Applet 1.4
-sided polygon inscribed in the circle, then we get the sequences of numbers
,
,.....,
.
