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:
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.
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
Sn= n/2{a +a + (n – 1)d}
\Sn = n/2 {2a + (n – 1)d}
To gain full access to the note: DOWNLOAD FILE
Do you want to study Agricultural Extension in OOU? Before you apply for the OOU…
Do you want to study Agricultural Economics in OOU? Before you apply for the OOU…
Do you want to study Cooperative and Business Management in OOU? Before you apply for…
Do you want to study Home and Hotel Management in OOU? Before you apply for…
Do you want to study Animal Production in OOU? Before you apply for the OOU…
Do you want to study Crop Production in OOU? Before you apply for the OOU…