Sum To N Terms Of Special Series
Chapter Name : Sequences And Series |
Sub Topic Code : 104_11_09_07_01 |
Topic Name : Sum To N Terms Of Special Series |
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Sub Topic Name : Sum To N Terms Of Special Series |
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Introduction
You
will learn how to find sum of some special series such as natural numbers,
squares of natural numbers.
Pre-Requisites:
Idea about sequences and series, sum of N terms of an AP and GP.
Activity:
Find
the sum of squares of first 100 natural numbers.
Real Life Question:
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Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Sum of n terms of an AP | The sum of n terms of an AP is defined as the summation of all the n terms of the series. It is given by: S= n/2 [ 2a+(n-1)d ] |
| Sum of n terms of a GP | Let ‘a’ be the first non zero term of a GP and ‘r’ be its common ration then Sn, the sum of n terms is denoted by: Sn = a+ ar + ar2 + …………..+ arn-1 S_n= (?a(1-r?^n))/(1-r) or S_n= (?a(r?^n- 1))/(r-1) |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Math library | To know about Sum to N terms of a special series. |
Real life uses :
These
methods are employed to find the sum of some special series which follow a
definite pattern.
Places to visit :
Math
libary
Practical examples around us
| Examples | Explainations |
|---|---|
| Stock market | Summation of numbers. |
What you learn in Theory:
How
to find the sum of any special series.
What you learn in Practice:
How
to apply sum of N terms of a AP/GP to find sum of special series.