3-The following pattern of numbers is called Pascal's triangle. 1 1 1 12 1 1 331 14641 The numbers at the edge of the triangle are all 1, and each number inside the triangle is the sum of the two numbers above it. Write a procedure that computes elements of Pascal's triangle by means of a recursive process.

6) Write a recursive function to calculate the summation of numbers from 1 to n. For exampleif the user enters 5, your program would add 1+2+3+4+5 and print out the answer 15.7) Write a recursive program to calculate Fibonacci numbers. Use the definition of a Fibonaccinumber where F(n) = F(n-1) + F(n-2). use java to code

T/F 1. Infinite recursion occurs where a recursive form lacks a base case.

Python Using recursion only No loops Note that in a correct solution the isdigit method or in operator will never be applied to the entire string s. The function must return and not print the resulting string. def getDigits(s):

CS211 Non-recursive solution for Towers of Hanoi Using the algorithm discussed in class, write an iterative program to solve the Towers of Hanoi problem. The problem: You are given three towers a, b, and c. We start with n rings on tower a and we need to transfer them to tower b subject to the following restrictions: 1. We can only move one ring at a time, and 2. We may never put a larger numbered ring on top of a smaller numbered one. There are always 3 towers. Your program will prompt the user for the number of rings. Here is the algorithm. Definition: A ring is "available" if it is on the top of one of the towers. Definition: The "candidate" is the smallest available ring that has not been moved on the most recent move. The first candidate is ring 1. The Algorithm: 1. Find the candidate. 2. Move the candidate (right or left, depending if the number of rings is odd or even) to the closest tower on which it can be placed. Move "around the circle" if necessary. 3. If not done, go back…

Complete the following program Multiply.java. This program uses recursion to multiply two numbers through repeated addition. The output should look exactly like what is pictured below. The code should be completed where it states "complete here"

Part (1) Write a recursion method named CalculateSeries, that will receive one integer valuen as parameter. The method will calculate and return the term n in the following series: T(0)= 0 T(n)= 2 T(n-1) +1 Part (2) Write the main method to test your method. Enter n >> 5 T(5) = 31 %3D

T/F 11. A recursion will still be replaced by an iteration and the other way around.

Java source code writing - a recursive algorithm. Please use non-recursive and recursive ways to compute the nth Harmonic number, defined as H. Turn in your java source code file with three methods, including one main() method.

The Fibonacci algorithm is a famous mathematical function that allows us to create a sequence of numbers by adding together the two previous values. For example, we have the sequence:1, 1, 2, 3, 5, 8, 13, 21…Write your own recursive code to calculate the nth term in the sequence. You should accept a positive integer as an input, and output the nth term of the sequence.Once you have created your code, add comments describing how the code works, and the complexity of any code you have created.