;; CS101, Spring 2013
;; Lab 4

;; Writing recursive functions over numbers.

(display "\n         CS101 Lab 4, Spring 2013\n")
(display "\n        PLEASE WRITE YOUR NAME HERE\n\n")

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(display "Problem 1: Computing the sum of squares from 1 to n.\n\n")
;    
;   Problem 1: Function SUM-SQUARES
; 
;    Write a function that consumes a positive natural number and
;    returns the sum of squares as follows:  1^2 + 2^2 + ... + n^2     
;    
;    Think about the smallest possible value in this equation for any
;    given value of n, a positive natural number. That number will be
;    the base case.
;    
;    The recursive case will be run for every value of n greater than
;    the base case. 
;    
;    Begin by writing a contract, header, purpose, and pre-function
;    test suite for function sum-squares. Then write the function and 
;    test it on different inputs in printf statements.
;    
;    Use regular numeric recursion in your solution.  
;    


; Contract:
; Header:
; Purpose:

; Pre-function tests:

; Function definition:

; Post-function printf's:


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(display "Problem 2: Computing the geometric sum from 0 to n.\n\n")
; 
; PROBLEM 2:  Function GEOM-SUM
; 
;     A geometric sum has the following form:
; 
;                 1 + x + x^2 + x^3 + ... + x^n
;         
;     Recall from math classes that x^0 = 1 and x^1 = x. If you
;     try to number the expressions in the equation above, you
;     start with an exponent of 0 and end with an exponent of n. 
;     
;     Define a recursive function, GEOM-SUM, that computes sums of 
;     the form shown above.
;     
;     Since you are writing a recursive function in which n is the 
;     recursive parameter, you should choose to write the function 
;     such that n gets closer to 0 on each recursive call.
;     
;     This function should consume 2 parameters, the value of x and   
;     the value of n.
; 
;     Follow the design recipe when writing this function:
;     Write the contract, header, purpose, pre-function tests 
;     (check-within statements), function definition, and post-
;     function printf's.
;      
;     Use regular numeric recursion in your solution.
;     


; Contract:
; Header:
; Purpose:

; Pre-function tests:

; Function definition:

; Post-function printf's:

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(display "Problem 3: Computing an alternating series.\n\n")
;  
; Problem 3: Function SUM-ALT-SERIES
; 
;   The alternating series looks like this:
; 
;                  1 - 1/2 + 1/3 - 1/4 + 1/5 - ...
; 
;   Mathematicians tell us that the more terms you include, the
;   closer the sum gets to the value ln(2) (i.e., the natural
;   logarithm of 2), which is about 0.693.
; 
;   For this problem, define a RECURSIVE function, called
;   SUM-ALT-SERIES, that takes a single input, N.  You may 
;   assume that N is a positive integer.  The output of
;   SUM-ALT-SERIES should be a sum of the form:
; 
;              1 - 1/2 + 1/3 - 1/4 + 1/5 - ... (+/-)1/N
; 
;   For example, if N is 3, then the output should be the
;   result of evaluating:
; 
;                      1 - 1/2 + 1/3 
; 
;   which equals approximately 0.833333333333.
; 
;   Since this function produces a real number for some values
;   of N, you should use the CHECK-WITHIN pre-function tester 
;   that gives the expected result followed by the allowable 
;   error.
; 
;   What is the base case for this function?
; 
;   ==> Notice that the sign of the Nth term depends on the 
;       value of N, specifically whether N is even or odd.
;       This implies that the recursive clause in this 
;       function will either itself contain a decision
;       statement OR you will write 2 recursive clauses.           
;   
;   ==> You can use the built-in odd? or even? function in your
;       solution. 
;       
;   ==> When your function runs, try it out on large values 
;       of N, say 1000.  Compare the output in test expressions
;       to (log 2), Racket's built-in LOG function, called with
;       argument 2 to compute the natural logarithm of 2. As 
;       the argument to sum-alt-series gets larger, the value
;       returned should get closer to (log 2).  Use the exact->
;       inexact function in your printfs for large values of n.
;       
;   Use regular numeric recursion in your solution. 
; 



; Contract: 
; Header:  
; Purpose:  

; Pre-function tests:

; Function definition:

; Post-function printf's:


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