# programaming-in-java-

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

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

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

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

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

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

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

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

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

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

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**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.**

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

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**public static ****String dec2Bin(****int ****value)**

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