Write the integer 125 in the manner that every positive integer can be representable as a...
Write a C program to compute and print Fibonacci values for some integers. You can assume that all input numbers are positive integers. The Fibonacci numbers are defined as follows: The first two Fibonacci numbers are 1 and 1. Any Fibonacci number after the first two numbers is the sum of its two predecessors. The Fibonacci numbers can be listed as the following sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... It is clear...
Write a program that computes the Fibonacci number for some input integer. (See segments 7.37 – 7.41 in your book for some info on the Fibonacci sequence or you can look it up on the Internet). The sequence is defined as the first two elements are each 1, after that each element in the sequence is the sum of the previous two elements. The first few numbers of the sequence are 1,1,2,3,5,8,13,21,34,55,… Your assignment is to write a program with...
Use strong induction to show that every positive integer can be written as a sum of distinct powers of two (i.e., 20 = 1; 21 = 2; 22 =4; 23 = 8; 24 = 16; :). For example: 19 = 16 + 2 + 1 = 2^4 + 2^1 + 2^0 Hint: For the inductive step, separately consider the case where k +1 is even and where it is odd. When it is even, note that (k + 1)=2 is...
c++ fibonacci code using loops Here are 8 Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21 Note that the first Fibonacci number is 1, F(1) = 1 The second Fibonacci number is 1, i.e. F(2) = 1 Other Fibonacci numbers in the sequence is the sum of two previous Fibonacci numbers. For example F(3) = F(2) + F(1). In general F(n) = F(n-1) + F(n-2) Write a program to do the following tasks. User entries are shown in...
CH Question 1. Implement a recursive method fibo that takes an integer num as a parameter and returns the nth Fibonacci number. Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, ... is an infinite sequence, where first 2 numbers are 1 and every subsequent number is equivalent to the sum of the previous two. Question 2. Implement a recursive method mult that takes two positive integer parameters, x and y and returns their product For example mult(2,3) returns 6....
Prove by induction that for every positive integer n, the following identity holds: 1+3+5+...+(2n – 1) = np. Stated in words, this identity shows that the sum of the first n odd numbers is n’.
1. (sumFrom1.cpp) Write a program that will ask the user for a positive integer value. The program should use the for loop to get the sum of all the integers from 1 up to the number entered. For example, if the user enters 50, the loop will find the sum of 1, 2, 3, 4, ... 50. If the user enters a zero or negative number, a message should be given and the program should not continue (see Sample Run...
A java program Write a program that prompts for and reads in a positive integer into a variable n. Your program should then sum the first n ODD integers and display the sum. For example, if 3 is entered for n, your program should display the the sum 1 + 3 + 5. If 5 is entered, your program should display the sum 1 + 3 + 5 + 7 + 9. What is the...
Write a recursive function named arithmeticSum that takes a positive integer parameter n and returns the sum of the integer numbers from 1 to n Please write in C++
3. Consecutive Sums a. (4 pts) Write 90 as the sum of consecutive positive integers in as many ways as possible. b. (4 pts) If a number can be written as n (d)(t) where d is an odd number of the form 2k + 1 and d is greater than 1, show symbolically how n can be written as the sum of consecutive numbers. Illustrate this with one example from part a. c. (4 pts) State a conjecture identifying the...