Categories: Lesson Notes

SS1 Second Term Further Mathematics Lesson Note – Series

The content is just an excerpt from the complete note for SS1 Second Term Further Mathematics Lesson Note – Series. Check below to download the complete DOCUMENT

WEEK 2

CLASS: SS1

TOPIC: SERIES

CONTENT:

  1. Definition of series.
  2. Arithmetic series
  3. Geometric series
  4. Sum to infinity

Sub – Topic: DEFINITION OF SERIES/ARITHMETIC SERIES

Series is the summation (addition) of the terms of a sequence. For example, the series equivalent of the sequence 1,2,3, 4, is 1+2+3+4+…. If the sequence contains finite numbers of terms, then the corresponding series is finite. If the sequence contains infinite numbers of terms, then the corresponding series is infinite.

Arithmetic Series:

These are series formed from an arithmetic progression. e.g.

1 + 4 + 7 + 10 + …

In general, if Sn is the sum of n terms of an arithmetic series then

Sn = a + (a + d) + (a + 2d) + … + (l – d) +l   …………………….. (1)

Where l is the nth term, a is the first term and d is the common difference.

Rewriting the series above starting with the nth/last term, we have.

Sn = l +(l – d) + (l – 2d) +… + (a + d) + a  ………………………….(2)

Adding equation (1) and (2) we have

2Sn = (a + l) + (a + l) + … + (a + l) + (a + l) in n places

2Sn = n(a + l)

\Sn = n/2(a + l)  

But l is the nth term i.e a + (n – 1) d

Snn/2{a +a + (n – 1)d}

\Sn = n/2 {2a + (n – 1)d}

To gain full access to the note: DOWNLOAD FILE

Sunday

Share
Published by
Sunday

Recent Posts

List of Universities Offering Veterinary Medicine in Nigeria

Veterinary medicine is the branch of medicine that deals with the prevention, diagnosis, and treatment…

2 months ago

List of Universities Offering Anthropology in Nigeria

Anthropology is the scientific study of human beings and their cultures. It encompasses a wide…

2 months ago

List of Universities Offering Sociology in Nigeria

Sociology is the scientific study of human society, culture, and behavior. It examines the social…

2 months ago

List of Universities Offering Social Work in Nigeria

Social Work is a profession dedicated to helping individuals, families, and communities to cope with…

2 months ago

List of Universities Offering Religious Studies in Nigeria

Religious studies is an academic discipline that explores the beliefs, practices, and history of various…

2 months ago

List of Universities Offering Public Administration in Nigeria

Public administration is the field of study and practice that focuses on the organization and…

2 months ago