**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 / (****2***i ***+ ****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.**