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Flashcards covering key concepts of Mathematical Induction based on lecture notes.
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Principle of Mathematical Induction
A method used to prove mathematical statements for all positive integers.
Base Case
The initial step showing that a statement holds true for n=1.
Inductive Step
Assuming a statement is true for n=k and proving it for n=k+1.
Inductive Hypothesis
The assumption that a statement is true for a specific positive integer k.
Natural Numbers
The set of positive integers starting from 1.
Divisibility
A condition where one integer can be divided by another without leaving a remainder.
Summation
The operation of adding a sequence of numbers.
Type 1 Question
A question that involves proving a statement about summation or multiplication of sequences.
Type 2 Question
A question about statements involving divisibility by a natural number.
Type 3 Question
A question that involves proving inequalities for positive integers.