6) Write a recursive function to calculate the summation of numbers from 1 to n. For example if 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 Fibonacci number where F(n) = F(n-1) + F(n-2).

The following problems below require the utilization of recursion to be solved. Must also have comments. 1. Write a python program that determine the greatest common divisor of two numbers. 2. Write a python program that computes the value of a number to a power 'n'.

Please help me create a sierpenski triangle using recursion. Please comment the code explaining each line of code. The program must be completed in java if you can please also create a t squared fractal using java and recursion (you don't have to comment the code)

2. Consider a rectangle whose side lengths are two consecutive Fibonacci numbers. (Of course, neither of them is 0.) Such a rectangle could be, for example, 3 by 5, or 8 by 13, or 21 by 34, etc. (a) Give a recursive algorithm to dissect such a rectangle into squares such that no more than two of the resulting squares are the same size. (For example, if you had two 3 by 3 squares, you could have at most one 4 by 4 square.) Here's a specification for your algorithm: // Input: Two consecutive Fibonacci numbers f0, f1, representing an f0 by f1 rectangle, such that f0 <= f1. (Neither f0 nor f1 will be 0.) // Output: A list of integers representing side lengths of squares, such that the input rectangle can be dissected into squares of those sizes. No more than two of the squares can be the same size. Please be sure to give an English description of the algorithm along with pseu- docode, explaining the main points of its design, and a concise inductive argument for its correctness (i.e., say...

4

Q1. Write a recursive method to compute the following series: 1 1 f(i) =,+-++ 6. ... 2i Write a test program that displays f(i) for i = 1, 2, 3, 4, and 5. Sample run i = 1 i = 2 i = 3 i = 4 f(i) = 0.50 f(i) = 0.75 f(i) = 0.92 f(i) = 1.04 f(i) = 1.14

I would appreciate help with this question in Java please.

Make a code using Recursion The countSubstring function will take two strings as parameters and will return an integer that is the count of how many times the substring (the second parameter) appears in the first string without overlapping with itself. This method will be case insensitive. For example: countSubstring("catwoman loves cats", "cat") would return 2 countSubstring("aaa nice", "aa") would return 1 because "aa" only appears once without overlapping itself. public static int countSubstring(String s, String x) { if (s.length() == 0 || x.length() == 0) return 1; if (s.length() == 1 || x.length() == 1){ if (s.substring(0,1).equals(x.substring(0,1))){ s.replaceFirst((x), " "); return 1 + countSubstring(s.substring(1), x); } else { return 0 + countSubstring(s.substring(1), x); } } return countSubstring(s.substring(0,1), x) + countSubstring(s.substring(1), x); } public class Main { public static void main(String[] args) {...

write a code in java (using recursion)

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"

The 4th problem mimics the situation where eagles flying in the sky can be spotted and counted.FindEagles: a recursive function that examines and counts the number of objects (eagles) in aphotograph. The data is in a two-dimensional grid of cells, each of which may be empty (value 0) orfilled (value 1 to 9). Maximum grid size is 50 x 50. The filled cells that are connected form an object(eagle). Two cells are connected if they are vertically, horizontally, or diagonally adjacent. Thefollowing figure shows 3 x 4 grids with 3 eagles. 0 0 1 21 0 0 01 0 3 1 FindEagle function takes as parameters the 2-D array and the x-y coordinates of a cell that is a part ofan eagle (non-zero value) and erases (change to 0) the image of an eagle. The function FindEagleshould return an integer value that counts how many cells has been counted as part of an eagle and havebeen erased. The following sample data has two pictures, the first one is 3 x 4, and the second one is 5 x 5 grids. Notethat your program...

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

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.