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2 cards from this section. Quick, good the night before a test.
What is the base case in mathematical induction?
Think of the smallest number in the natural numbers.
Describe the inductive step.
It connects two consecutive numbers.
What is the base case in mathematical induction?
Consider the smallest integer in the set.
True or False: The inductive step proves the statement for all natural numbers.
Think of the inductive step as stepping to the next number only.
Prove by induction that for every n >= 1, 3^n > n^3.
Consider how exponents on both sides can reveal the inequality.
Show by induction that the Fibonacci sequence satisfies F(n) = F(n-1) + F(n-2) easily using n=2 as the base case.
Refer to the definition of Fibonacci to structure your proof.
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