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 +……..
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.
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.
