8. Write C++ program to show that the sum of the infinite series, which is converges to In 2. N 1 T = (2n + 1)(2n + 2) n=0 Compute the answer for N=50 and N=100
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- if n = 1 S(n) S(n//2) S(n – 1) if n is even; // is Python integer division if n is odd and n >1 Does Master Theorem apply to the recursive function S? Answer by writing either "yes" or "no" There is no need for extra explanations in this part.In C program We want to emulate that, too! Using a recursive function, make it so that we print the number we are currently in on a new line. When we encounter a number n divisible by 5, we print "YEHEY" and jump 7 steps forward. However when we encounter a number divisible by 8, we print "OHNO" and go back 6 steps. If it is divisible by both, we print "LUCKY" and jump 11 steps. Otherwise just move 1 step. Start at n=1 and continue doing this until you reach a number greater than or equal to the number entered by the user. Instructions: In the code editor, you are provided with a main() function that must ask the user for a number and calls the snake_ladder() function.This snake_ladder() function is a recursive function which should perform the functionality explained in the problem description above.This function is declared but is initially empty.Input 1. Stopping number Description Input the number to which the recursive function must stop Constraints The input is a positive integer…Write C++ program to show that the sum of the infinite series, which is converges to ln 2. ??= � 1(2??+ 1)(2??+ 2)????=0Compute the answer for N=50 and N=100
- Which of the following is the recursive definition for the function f(n)=2n with initial condition f(1) = 2? f(n) = 2n + f(n-1) f(n) = 2n - f(n-1) f(n) = 2n * f(n-1) f(n) = 2f(n − 1) Which of the following is the recursive definition for the function f(n)=5n+2 with initial condition f(1)=7? f(n) = 5n - f(n-1) f(n) = 5f(n-1) + 2 f(n) = 5n + f(n-1) f(n) = f(n-1) + 5In C program We want to emulate that, too! Using a recursive function, make it so that we print the number we are currently in on a new line. When we encounter a number n divisible by 5, we print "YEHEY" and jump 7 steps forward. However when we encounter a number divisible by 8, we print "OHNO" and go back 6 steps. If it is divisible by both, we print "LUCKY" and jump 11 steps. Otherwise just move 1 step. Start at n=1 and continue doing this until you reach a number greater than or equal to the number entered by the user. Instructions: In the code editor, you are provided with a main() function that must ask the user for a number and calls the snake_ladder() function. This snake_ladder() function is a recursive function which should perform the functionality explained in the problem description above. This function is declared but is initially empty. Input 1. Stopping number Description Input the number to which the recursive function must stop Constraints The input is a…Make it in Python Write a function factorial (n) that recursively calculates and returns n!n! = 1 * 2 * 3 .... (n-2) * (n-1) * nThe mathematical function of the faculty function f (n) is as follows: 1 n=0 f(n) n*f(n-1). n>0 The function must be recursively implemented to be correct.Your function should not take any inputs nor make any prints it solves the function while. number = int (input ())print (factorial (number))
- Make it in Python Write a function factorial (n) that recursively calculates and returns n!n! = 1 * 2 * 3 .... (n-2) * (n-1) * nThe mathematical function of the faculty function f (n) is as follows: 1 n=0 f(n) n*f(n-1). n>0 The function must be recursively implemented to be correct.Your function should not take any inputs nor make any prints it solves the function while. use this code to test number = int (input ())print (factorial (number))Write a programe in PYTHON to Write a recursive function that takes positive int n as its input and returns sum of the first n squares, i.e. .12 + 22 + ….. + N2.Write a recursive function for Euclid's algorithm to find the greatest common divisor (gcd) of two positive integers. gcd is the largest integer that divides evenly into both of them. For example, the gcd(102, 68) = 34. You may recall learning about the greatest common divisor when you learned to reduce fractions. For example, we can simplify 68/102 to 2/3 by dividing both numerator and denominator by 34, their gcd. Finding the gcd of huge numbers is an important problem that arises in many commercial applications. We can efficiently compute the gcd using the following property, which holds for positive integers p and q: If p > q, the gcd of p and q is the same as the gcd of q and p % q.
- Can you write a recursive c program that takes as an input a total of N integers and prints every subtotal that has a sum equal to zero (if exists). Also mention its complexity ex. input:N = {-10, -3, 1, 2, 4, 6) output: {-10, 4, 6}, {-10, -3, 1, 2, 4, 6}, {-3, 1, 2}Write a recursive C++ program to find the GCD of two numbers and using this write a function to find the L.C.M of two numbers in O(1) time. GCD function should contain one line of code. Please answer only if you can fulfill the conditions else I will downvote.Write a pseudo-code then implement a program in C/C++ to enter a natural number n and verify whether n is sphenic. Calculate the complexity of your program.Note: A sphenic number is a product of p*q*r where p, q, and r are three distinct prime numbers. Example: 30 = 2 * 3* 5; 42 = 2*3*7; 66 = 2*3*11