Concept explainers
A perfect square is a number that can be written as
a. Check that the following statement is true for 4 different cases. How many cases do you need to try to conclude that the statement is true?
“1 plus the product of any four consecutive whole numbers is always a perfect square”
b. Prove that the sum of first n odd numbers is a perfect square.
c. Find all perfect square numbers that are 9 more than some prime number. Explain how you know that you found all such square numbers. (Hint: Recall from Chapter 3 that
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Check out a sample textbook solutionChapter 4 Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
- Show that if the statement is assumed to be true for , then it can be proved to be true for . Is the statement true for all positive integers ? Why?arrow_forwardShow that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation can be proved to be true for n=k+1. Explain why this does not prove that the statement is true for all positive integers. Is the statement true for all positive integers? Why?arrow_forward
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