Mathematical Induction & Matrices. Free PDF download (1.3 MB) from the ExamineAI past papers library.
A free account is needed to download. Sign in or create one
This is the Mathematics study guide. It is a free study guide for revision.
TROCKERS
"Do not worry too much about your difficulties in Mathematics, I can assure you that mine are still greater." Albert Einstein.
MATHEMATICAL INDUCTION
COMPILED BY TARAKINO N.P. (Trockers)
Definition: It is a method of proof in which a statement is proved for one step in a process, and it is shown that if the statement holds for that step, it holds for the next.
STEPS
i. Base Case/Initial Stage
Show it is true for $n=1, n=2$ etc and give a conclusion of this stage.
ii. Assumption/Hypothesis Stage
Suppose/ assume the statement is true for $n=k$.
iii. Thesis Stage
Stating the result for $n=k+1$.
iv. Proof Stage
Proving true for $n=k+1$. Use the thesis stage and the hypothesis stage to get the required result. Give a conclusion of this stage.
v. Conclusion Stage
State four conditions clearly: $n=1, n=k, n=k+1$ and $n \in \mathbb{Z}^{+}$
Areas to consider
- Divisibility
- Series/Summations
- Matrices
- Integration
- Differentiation
Compiled by Nyasha Patrick Tarakino - BSc. (Hon's) Mathematics (M.S.U.) +263772978155/+263717267175