Sequences and Induction
Mathematical induction is a powerful method used to prove statements for all integers. It involves two steps: proving the statement true for a base case, and then showing that if it holds for one integer, it also holds for the next integer in line. This technique is illustrated through the analogy of climbing a ladder: ensuring you can reach the first rung and then proving that you can always reach the next rung. By following these steps, mathematical induction allows for the validation of conjectures across all integer values.
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Sequences and Induction Mathematical Induction
Mathematical Induction 1. You know you can reach the first rung. 2. If you can reach a rung you can always reach the next one.
Mathematical Induction To prove that P(n) is true for all integers n a, complete two steps: 1. Prove that P(a) is true for some value, a. 2. Show that, if P(k) is true then P(k + 1).
Mathematical Induction + P ( 1) ( ( ) n P n P n ( 1)) ( ( )) P n n
