Series
Chapter Name : Sequences And Series |
Sub Topic Code : 104_11_09_03_01 |
Topic Name : Series |
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Sub Topic Name : Series |
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Introduction
Everything in this world that follows a pattern is a sequence. Prime numbers for example is a sequence. Series is a notation to write a sequence.
Pre-Requisites:
Idea about sequences.
Activity:
Assuming a generation gap of 30 years, find the number of ancestors i.e. parents, grandparents, great grandparents, etc. over a span of 300 years. Write it in the form of a series!
Real Life Question:
Find the total number of triangles after next two iterations of a sierpinski triangle?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Sequence | A sequence can be regarded as a function whose domain is the set of natural numbers or a subset of it. |
| nth term of the Sequence | The nth term is the number at the nth number in the sequence. |
| Series | Let a1, a2, a3, …….. an be a sequence. Then the expression a1+a2+ a3+ …….. an is called the series associated with the sequence. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Calculator | Construct a sequence of numbers whose first term is 1 and second term is 1 and every consecutive term is sum of previous two terms. And find the sum of 15 terms. |
Real life uses :
Series have been used in the trading algorithms, applications and strategies. To model spiral of waves, breeding of animals and branching of tees etc.
Places to visit :
Math Lab.
Practical examples around us
| Examples | Explainations |
|---|---|
| 1. Fibonacci Sequence | 1 + 1 + 2 + 3 + 5 + 8… First two terms are ‘1’ and every next term is the sum of preceding two numbers. |
| 2. Prime Numbers | 2 + 3 + 5 + 7 + 9… The prime numbers is a series of numbers having a special property. |
What you learn in Theory:
What is a series, infinite and finite series?
What you learn in Practice:
How to write a series and find the nth term and how to represent it.