Practice - Proceeding with Induction
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Practice Questions
Test your understanding with targeted questions
What is the arithmetic mean of 3 and 9?
💡 Hint: Add the two numbers together and divide by 2.
Give an example of a positive integer and its binary representation as a sum of distinct powers of two.
💡 Hint: Remember each integer has a unique binary form.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the formula that defines the relationship between AM and GM?
💡 Hint: Think of how averages behave.
True or False: Every positive integer has a unique binary representation as a sum of distinct powers of two.
💡 Hint: Consider how binary numbers correlate to decimal.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Using induction, determine a formula for proving that the sum of the first n odd numbers equals n^2.
💡 Hint: Sum the k odd numbers and add the next to the result.
Give a rigorous proof that the infinite series 1/2^n converges, using bounds established via induction.
💡 Hint: Use geometric series properties.
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