# 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.

## 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°)