State the principle of mathematical induction
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1) when a statement is true for a natural number n = k,
then it will also be true for its successor, n = k + 1; and
2) the statement is true for n = 1; then the statement will be true for every natural number n.
then it will also be true for its successor, n = k + 1; and
2) the statement is true for n = 1; then the statement will be true for every natural number n.
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HEY THERE,
Basis Step: Prove that P( ) is true. Induction: Prove that for any integer , if P(k) is true (called induction hypothesis), then P(k+1) is true. The first principle of mathematical induction states that if the basis step and the inductive step are proven, then P(n) is true for all natural number .
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Basis Step: Prove that P( ) is true. Induction: Prove that for any integer , if P(k) is true (called induction hypothesis), then P(k+1) is true. The first principle of mathematical induction states that if the basis step and the inductive step are proven, then P(n) is true for all natural number .
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