# applied-programming-homework-1

You are to design a recursive algorithm and implement in Java, to do the following computation.

You program should have main method, then call each of the following recursive method

I need a hard copy to, showing the Source Code and the output runs.

a. (Sum series) Write a recursive method to compute the following series:

m(i) = 1 + 1/2 + 1/3 + â€¦.. + 1/ i

Write a test program that displays m(i) for i = 1, 2, . . ., 10.

b.. (Sum series) Write a recursive method to compute the following series:

m(i) = 1/ 3 + 2/ 5 + 3/ 7 + 4 / 9 + 5/11 + 6/ 13 + â€¦. + i / (2i + 1)

Write a test program that displays m(i) for i = 1, 2, . . ., 10.

c. (Sum series) Write a recursive method to compute the following series:

m(i) = 1 / 2 + 2 / 3 + â€¦â€¦+ i / (i + 1)

Write a test program that displays m(i) for i = 1, 2, . . ., 10.

d. (Find the largest number in an array) Write a recursive method that returns the largest integer in an array. Write a test program that prompts the user to enter a list of eight integers and displays the largest element.

e. (Decimal to binary) Write a recursive method that converts a decimal number into a binary number as a string. The method header is:

public static String dec2Bin(int value)

Write a test program that prompts the user to enter a decimal number and displays its binary equivalent.