A common example of a recursive formula is one to compute the sum of the first n integers, 1 + 2 + 3 + … + n. The recursive formula can be expressed as 1+2+3+…+n=n+(1+2+3+…+(n – 1)) Write a static method that implements this recursive formula to compute the sum of the first n integers. Place the method in a test program that allows the user to enter the values of n until signaling an end to execution. Your method definition should not use a loop to add the first n integers.
This Project is also very easy to write as a recursive algorithm. The base case returns one and any other case adds the number passed to it to the number returned by a recursive call with the number passed to it reduced by one. Note that the program loops until the user enters a positive integer since the progression is defined only for positive integers.
See the code in ArithmeticProgression.java.
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