~ 6 Sum of ik Intro In discrete math we learn that the sum of integer from 1...n is given by and and As you may notice, one can actually show that has is a polynomial of degree k +1. i=1 i=1 2 = n(n -1 2 འ Σί IM³ i=1 33 n° 2 12 - + n² n ས + 26 n 53 = = (n(n − 1)) ² = 2 — n4 4 i=1 To calculate the sum if we use for loop and calculate the left hand side it will be O(n). But if we use the right hand side we can calculate it in O(1). So, calculating it with a closed form is a much better approach. But as you recall getting the close formed formula is quite difficult to do by hands. In this problem we will use legendre polynomial to find it. Problem Use what you learn about Legendre Method and write a function that takes in n and k and calculate in O(k) (NOT O(n)). Warning: don't try to sum up too far as it can cause integer overflow. 1 n i=1 ik Python

In Java using recursion, create a program with a GUI that will allow a user to enter five numbers. The program will provide the product of all five numbers using recursive methods.

%matplotlib inlineimport mathimport numpy as npfrom matplotlib import pyplot as pltdef bad_poisson(lmd, k):    return pow(lmd,k)*math.exp(-lmd)/math.factorial(k)# bad_poisson(1000,1000) # uncomment to see it breaks

Java Programming language Please help me with this. Thanks in advance.

There is no difference between an array and an arraylist   True   False

BAGEL FILES     import javax.swing.JFrame; public class Bagel{//-----------------------------------------------------------------// Creates and displays the controls for a bagel shop.//-----------------------------------------------------------------public static void main (String[] args){JFrame frame = new JFrame ("Bagel Shop");frame.setDefaultCloseOperation (JFrame.EXIT_ON_CLOSE); frame.getContentPane().add(new BagelControls()); frame.pack();frame.setVisible(true);}}       import java.awt.*;import java.awt.event.*; import javax.swing.*; public class BagelControls extends JPanel{private JComboBox bagelCombo;private JButton calcButton;private JLabel cost;private double bagelCost;public BagelControls(){String[] types = {"Make A Selection...", "Plain","Asiago Cheese", "Cranberry"};bagelCombo = new JComboBox(types);calcButton = new JButton("Calc");cost = new JLabel("Cost = " + bagelCost);setPreferredSize (new Dimension (400,…

Main difference between an array and an ArrayList is that an ArrayList can store more data types an ArrayList can store more elements an ArrayList executes faster for retrieval and insertion an ArrayList takes care of the memory management automatically an ArrayList uses positions and an array uses indices

Java

2. Problem 2: In this problem you will test our "in class" version of Gaussian elimination against the version in numpy. Use both codes to solve some randomly chosen linear systems of size N 10, 20, 40, 80, 160, 320, 640, 1280, 2560, and 5120. Depending on your computer, the last two may or may not work. If they don't, just say so in your report. If you computer can do N- 10240 then try this as well. Note that in cach case N 10 * 2k for k = 1,..., 10. That is, each time we are doubling the size of the matrix. abone Plot the results as two curves. Our code in red and numPy in bluc. (Or whatever colors you prefer). Can you guess the function which governs the runtime? Based on this guess, how long would it take to do N 40960 using numPy? N=81920?