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.
If 𝑇1; 𝑇2; 𝑇3; … … … 𝑇𝑛 denotes a sequence of which the 𝑛𝑡ℎ term is 𝑇𝑛 , then the 𝑇1 + 𝑇2 + 𝑇3 … … … + 𝑇𝑛 is called a series.
A series is given by adding terms of a particular sequence.
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
Full explanation on this topic and how to answer questions in an exam.
Notes for Inventory valuation.
- Prove (accepting results established in earlier grades):
• 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);
• That equiangular triangles are similar;
• That triangles with sides in proportion are similar; and the Pythagorean
Theorem by similar triangles
- Revise the following including grade 10 concepts:
• The equation of a line through two given points;
• The equation of a line through one point and parallel or perpendicular to
a given line; and
• The inclination (θ) of a line, where 𝑚 = tan 𝜃 is the gradient of the line (0° ≤ 𝜃 ≤ 180°)
- Apply the equation
that defines a circle with radius r and centre (a ; b)
3.Determine the equation of a tangent to a given circle.