this is java problem. class named RecursionExamples with a number of empty methods corresponding to the 5 recursive methods described below. A main is provided for testing.

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public class RecursionExamples {

public static void main(String[] args) {

}

public static double sumSeries(int n) {

return 0.0;

// *** WRITE CODE HERE ***

}

public static void printReverse(String s, int n) {

// *** WRITE CODE HERE ***

}

public static void printReverse2(String s, int n) {

// *** WRITE CODE HERE ***

}

private static void printReverse2(String s, int n, int loc) {

// *** WRITE CODE HERE ***

}

public static int countDigits(String s, int low, int high) {

return 0;

// *** WRITE CODE HERE ***, can use helper, or not

}

public static int countCode(String msg, String code ) {

return 0;

// *** WRITE CODE HERE ***

}

private static int countCode(String msg, String code, int pos ) {

return 0;

// *** WRITE CODE HERE ***

}

}

a. Write a recursive method with this signature: public static double sumSeries(int n) that returns the sum of the series: 1 2 1 1 +--?i...-?, if i is even-, b. Write a recursive method with this signature (do not use a helper method): public static void printReverse (String s, int n) that prints tuples of size n from the string in reverse. Examples: Input' "3412",2 ("789456123".3)-- "7456123",3 ("abcdefghijklmnopqrstuvwxyz",10) Output 1234 123456789-+ 1234567+ qrstu hijklmnopabcdef* c. Write a method with this signature pub is static void printReverse2(String s, int n) {4 that utilizes this recursive helper method