programaming-in-java-

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

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

m(i) =1 +1/2 +1/3 + ….. + 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 + …. + 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 + ……+ 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.