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Chapter 14: Problem 1
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Write a recursive function definition for the following function: int squares(int n); //Precondition: n >= 1 //Returns the sum of the squares of numbers 1 through n. For example, squares (3) returns 14 because \(1^{2}+2^{2}+3^{2}\) is 14
Redefine the function power so that it also works for negative exponents. In order to do this you will also have to change the type of the value returned to double. The function declaration and header comment for the redefined version of power is as follows: double power \((\text { int } x, \text { int } n)\) //Precondition: If \(n<\theta\), then \(x\) is not \(\theta\) //Returns \(x\) to the power \(n\) Hint: \(x^{-\mathrm{n}}\) is equal to \(1 /\left(x^{\mathrm{n}}\right)\)
Write a recursive void function that takes a single int argument \(n\) and writes integers \(n, n-1, \ldots, 3,2,1 .\) Hint: Notice that you can get from the code for Self-Test Exercise 4 to that for Self-Test Exercise 5 (or vice versa) by an exchange of as little as two lines.
Write a recursive void function that takes a single int argument \(n\) and writes the integers \(1,2, \ldots, n\)
Write a recursive void function that has one parameter which is a positive integer and that writes out that number of asterisks '*' to the screen all on one line.
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