Series

This topic studies sequences and series, including arithmetic and geometric progressions. Learners will find general terms, sums, and apply these concepts in problem-solving.

Learning Outcomes:
The learner should be able to:

• Define and distinguish between arithmetic and geometric sequences and series.
• Derive an Arithmetic Progression (A.P.) from terms of a sequence.
• Derive the formula for finding the sum and the nth term of an A.P.
• Derive expressions for nth term and the sums of a (G.P).
• Analyse convergence of G.P to generate the sum to infinity of a G.P.
• Calculate the sum of finite and infinite series where applicable.
• Use summation notation to determine the sum of any series.
• Use Socratic circle to deeply analyse the series
• Discuss the applications of G.P to real- world problems such as compound interest, spread of disease, cell division, radioactivity decay.
• Apply the logical steps to establish the truth of a mathematical statement.
• Use proof by induction to determine the validity of mathematics statements.
• Generate Pascal’s triangle to expand the forms (a + b)ⁿ for n=1,2,3, …
• Generate coefficients of terms in the expansion.
• Deduce the binomial theorem and use it to expand different functions.
• Expand binomial expressions in ascending and descending order.
• Compute roots of numerical values and state range of validity of binomial expansion.
• Apply the binomial theorem to solve real-world problems such as stochastic models.