Grade 12 Lessons Archives - Edublush Virtual Academy

Infinite Series

This is a series with infinity number of terms.

NB. If one added infinity number of terms of an arithmetic series, the sum becomes a very large positive number which increases as more and more terms are added e.g. 2 + 4 + 6 + 8 + 10 +……..

Since the sum of terms increases towards a very large positive hence the sum to infinity does not exist. We call that series a Divergent series.

NB. An infinity geometric series converges under certain circumstances. Consider the following cases.

CASE 2. Geometric series π‘Ÿ < 1 e.g. π‘Ÿ = 2 If π‘Ž = 1 ; ∴ 1 + 2 + 4 + 8 + 16 +…….
𝑆1 = 1
𝑆2 = 3
𝑆3 = 7
𝑆4 = 15
As more and more terms are added the 𝑆𝑛 becomes bigger and bigger (large positive). Since the sum is not approaching a particular value (figure) then the series is said to diverge and its sum to infinity does not exist.
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Definition Of A Series

If 𝑇1; 𝑇2; 𝑇3; … … … 𝑇𝑛 denotes a sequence of which the π‘›π‘‘β„Ž term is 𝑇𝑛 , then the 𝑇1 + 𝑇2 + 𝑇3 … … … + 𝑇𝑛 is called a series.

A series is given by adding terms of a particular sequence.

Symbols

𝑆𝑛 Denotes the sum of the first in terms

𝑆10 means the sum of the first 10 terms in the sequence.

𝑆10 = 𝑇1 + 𝑇2 + 𝑇3 … … … + 𝑇10

HTML Lesson

Full explanation on this topic and how to answer questions in an exam.

Notes for Inventory valuation.

Euclidean Geometry Grade12 Lesson2

  1. Prove (accepting results established in earlier grades):
    β€’ That a line drawn parallel to one side of a triangle divides the other two
    sides proportionally (and the Midpoint Theorem as a special case of the converse of this theorem);
    β€’ That equiangular triangles are similar;
    β€’ That triangles with sides in proportion are similar; and the Pythagorean
    Theorem by similar triangles
No need to write down the notes.You can check the notes at the bottom

Analytical Geometry Grade12 Lesson1

  1. Revise the following including grade 10 concepts:
    β€’ The equation of a line through two given points;
    β€’ The equation of a line through one point and parallel or perpendicular to
    a given line; and
    β€’ The inclination (ΞΈ) of a line, where π‘š = tan πœƒ is the gradient of the line (0Β° ≀ πœƒ ≀ 180Β°)
No need to write down the notes.You can check the notes at the bottom