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Summary PRE CALCULUS - Series
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The document is a summary discussion on the topic about SERIES. The different types of Series, like the arithmetic and geometric series, and there patterns. Techniques on identifying and computation on a missing value/s in a given series and sequence. This document summary includes sample computati...

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Document information

  • June 19, 2023
  • 8
  • 2022/2023
  • Summary

Subjects

  • stem
  • stem 11
  • shs
  • senior high school
  • calculus
  • pre calculus
  • series
  • mathematics
  • grade 11

Written for

  • Secondary school
  • Pre-Calculus
  • 4
All documents for this subject (21)

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, WHAT ABOUT SERIES?
What exactly is a series? Actually, a series in math is simply the sum of the various numbers or
elements of the sequence. For example, to make a series from the sequence of the first five
positive integers 1, 2, 3, 4, 5 we will simply add them up. Therefore 1+ 2+ 3+ 4+ 5 is a series.
So, series of a sequence is the sum of the sequence to some given number of terms, or sometimes
till infinity. It is often written as Sn.


Example:

If the sequence is 2, 4, 6, 8, 10,……

then the sum of the first 3 terms: S3=2+4+6

S3 = 12. Sn = n/2 * (2a1 + (n-1)d)


A sequence is a list of numbers or terms, separated by commas (,)

5, 10, 15, 20, 25

2, -2, 2, -2, 2

A series represents the sum of the terms of a sequence (separated by "+" or "_" sign).

 5+10+15+20 +25 =75
 2-2+2 2+2 =2



The sum of the first n terms in an arithmetic sequence is

(n/2) ⋅ (a₁ +aₙ)
It is called the arithmetic series formula.

NOTE:

 A series can be highly generalized as the sum of all the terms in a sequence. However,
there has to be a definite relationship between all the terms of the sequence.

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