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in kotlin, Write two versions of the recursive summation function (that is, take an int parameter n and calculate the sum of all integers from 1 to n). One version should use a block body, and the other should use an expression body. Test the functions using a main()
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- Write recursive functions for the following equations:a. Harmonic number is defined by the equationb. Fibonacci numbers are defined by the formula:FN = FN-2 + FN-1, for N ≥ 2 with F0 = 0 and F1 = 1Write a recursive function, reverseDigits, that takes an integer as a parameter and returns the number with the digits reversed. Also, write a program to test your function.write a recursive function named choose (int n,int k) that will compute and return the value of the binomial coefficient. write it as a C++ function on the computer.
- Write a recursive function that returns a value of 1 if its string argument is apalindrome and zero otherwise.* Note that for the function parameters, you need to accommodate for the shrinkingstring, so that the string shrinks both from beginning and end after each recursive call.** Think about the simple cases or base cases. The 2 base cases have conditions thatwould return 0 and return 1 independently.For the palindrome, create a driver program. First ask the user to enter anystring through the keyboard. Then remove all the spaces and punctuations from thestring. Also, remove any letter capitalization from the string. Finally, pass the string tothe palindrome function through a function call.Write a recursive function called draw_triangle() that outputs lines of '*' to form a right side up isosceles triangle. Function draw_triangle() has one parameter, an integer representing the base length of the triangle. Assume the base length is always odd and less than 20. Output 9 spaces before the first '*' on the first line for correct formatting. Hint: The number of '*' increases by 2 for every line drawn. Ex: If the input of the program is: 3 the function draw_triangle() outputs: * *** Ex: If the input of the program is: 19 the function draw_triangle() outputs: * *** ***** ******* ********* *********** ************* *************** ***************** ******************* Note: No space is output before the first '*' on the last line when the base length is 19. if __name__ == '__main__': base_length = int(input()) draw_triangle(base_length)Write a recursive function named sumSquares that returns the sum of the squares of the numbers from 0 to num, in which num is a nonnegative int variable. Do not use global variables; use the appropriate parameters. Also write a program to test your function.
- Question 2: Implementing a Recursive Function .Write recursive function, recursionprob(n), which takes a positive number as its argument and returns the output as shown below. The solution should clearly write the steps as shown in an example in slide number 59 and slide number 60 in lecture slides. After writing the steps, trace the function for “recursiveprob(5)” as shown in an example slide number 61. Function Output: >> recursionprob(1) 1 >> recursionprob(2) 1 4 >> recursionprob(3) 1 4 9 >>recrusionprob(4) 1 4 9 16Python only* Use recursive function*. Define concentricCircles with 4 parameters Use def to define concentricCircles with 4 parameters here is the specification for concentricCircles function: It draws a series of concentric circles, where the first parameter specifies the radius of the outermost circle, and the second parameter specifies the number of circles to draw. When viewed as nested rings, all rings should have the same thickness. The third and fourth parameters specify an outer color and an other color, respectively. The outer color is used for the outermost circle, and then every other circle in to the center alternates between that color and the other color. We will test both how many circles are drawn as well as whether the correct circles are drawn in the correct order. Hint: Each function call frame only needs to draw a single circle. Note that you must use the turtleBeads drawDot function to draw each circle Do not use any kind of loop Within the definition of…Python only* Use recursive function*. Define concentricCircles with 4 parameters Use def to define concentricCircles with 4 parameters here is the specification for concentricCircles function: It draws a series of concentric circles, where the first parameter specifies the radius of the outermost circle, and the second parameter specifies the number of circles to draw. When viewed as nested rings, all rings should have the same thickness. The third and fourth parameters specify an outer color and an other color, respectively. The outer color is used for the outermost circle, and then every other circle in to the center alternates between that color and the other color. We will test both how many circles are drawn as well as whether the correct circles are drawn in the correct order. Hint: Each function call frame only needs to draw a single circle. Note that you must use the turtleBeads drawDot function to draw each circle Do not use any kind of loop Within the definition of…
- Please can be handwritten. Question 2: Implementing a Recursive Function . Write recursive function, recursionprob(n), which takes a positive number as its argument and returns the output as shown below. The solution should clearly write the steps as shown in an example in slide number 59 and slide number 60 in lecture slides. After writing the steps, trace the function for “recursiveprob(5)” as shown in an example slide number 61. Function Output: >> recursionprob(1) 1 >> recursionprob(2) 1 4 >> recursionprob(3) 1 4 9 >>recrusionprob(4) 1 4 9 16Write a function which takes two integer parameters for values to be added together and returns the result by value. The function may not print anything or read anything directly from the user (i.e. no cin/cout in the function). Assume that the values passed to the function will not be negative, but could be 0 or positive, and will both be integers. The function must implement addition recursively, and cannot use the standalone + operator (only ++) or call any other functions.Write a recursive findodd function which returns the number of odd digits of given integer. Write a C program that tests function findOdd. (Your function must be recursive.) (Examples: findodd(22314675) returns 4, findOdd(113356) returns 5) Sample Input1: Sample Output1: 123312 Sample Input2: Sample Output2: 8. 11335573 Sample Input3: 1143 Sample Output3: