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Mathematical Induction - Problem 4
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
First, show your equation is true for the case n = 1 by substituting in one. Next, we write an assumption that the statement is also true for the kth term and replace all n's with k's. Third, we show that the statement is true for the "k + 1"th term, which means adding one more term, substituting what you had written when you assumed for k, and the simplifying. Finally, showing that the statement is true for "k + 1 " terms is sufficient to prove that it is true for all values of n.
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Sample Problems (6)
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