Using recursive functions, given three letters in the alphabet, get their permutations together with the combinations of any two letters from it. e.g. Input: xyz Output: xyz,xxy,xyx,yxx, xzy,yxz,yyz,yzy, zyy, yzx, zxy,zyx,xxz,xzx,zxx Input: xxy output: хху, хух, ухх Input: zzz Output: zzz

An arithmetic sequence starts 2, 5, . . . Write a recursive definition for this sequence using function notation.

in java Computing Powers, p(x,n)=xn1. Describe the definition of recursive function.oBase case(s)oRecursive case(s)2. Write the code

Give a recursive algorithm for finding the sum of the first n positive integers

Using any programming language, implement the Leibniz series; Leibniz( ) as a recursive function and interactive functions using both a for and while loop.

Write a program in Python that converts Euclid’s algorithm to find the greatest common divisor (GCD) of two positive integers to a recursive function named gcd.

Devise a recursive algorithm that finds the index of the smallest number in an array (sequence of numbers). in c++

Write a Python source code using recursion to find the greatest common divisor of two positive integers. Please name your function "recursive_gcd" that has two arguments (first integer, second integer) and return an int.

Write a recursive Python function named pgcd, to find and return the Greatest Common Divisor (GCD) of two numbers x and y passed in parameters. • Test it gcd (1234,4321) gcd (8192,192)

Recursion is a technique that calls the function by itself. Demonstrate and write a program to find the GCD of two numbers using recursion and mention the advantages of recursion.

IN PYTHON, Using recursion: ask the user for the length of a square and the character they want to use. Draw the square (similar to mini assignment #15 in functions part 3). Once the user creates the square with their specification, ask them if they want it to be smaller or larger and how many times. Draw all the squares growing in size to the specified range.

Define a recursive function that will add the sum of of the numbers in a finite sequence.

1. Given, nCr= n! (n-r)!r!" Write a function to compute nCr without recursion.