Lesson Category: Grade 12 Lessons
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 +β¦β¦..
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.
π1 = 1
π2 = 3
π3 = 7
π4 = 15
As more and more terms are added the ππ 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.
Β
Definition Of A Series
If π1; π2; π3; β¦ β¦ β¦ ππ denotes a sequence of which the ππ‘β term is ππ , then the π1 + π2 + π3 β¦ β¦ β¦ + ππ is called a series.
A series is given by adding terms of a particular sequence.
Symbols
ππ Denotes the sum of the first in terms
π10 means the sum of the first 10 terms in the sequence.
π10 = π1 + π2 + π3 β¦ β¦ β¦ + π10
HTML Lesson
Full explanation on this topic and how to answer questions in an exam.
Notes for Inventory valuation.
Euclidean Geometry Grade12 Lesson2
- 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
Analytical Geometry Grade12 Lesson1
- 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 = tan π is the gradient of the line (0Β° β€ π β€ 180Β°)