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3 cards from this section. Quick, good the night before a test.
What is the arithmetic mean of 3 and 9?
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.
Remember each integer has a unique binary form.
What is the formula that defines the relationship between AM and GM?
Think of how averages behave.
True or False: Every positive integer has a unique binary representation as a sum of distinct powers of two.
Consider how binary numbers correlate to decimal.
Using induction, determine a formula for proving that the sum of the first n odd numbers equals n^2.
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.
Use geometric series properties.
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