Question

4.2. The binomial theorem can be written as 4.3. W A d SS a'"-2h2 n(n - 1)(n - 2) 2! (a+ b)" = a"+1na-1hn(n-1) 3! Write a program for which a = 1 and 0 < b < 1 that uses the binomial theorem to calculate (a + b)" accurately to eight decimal places. Your pro- gram should also calculate (a + b)" using the pow() function. Make s that your program checks for b being between 0 and 1. (Note: This is converging series.) l sisbsoralua

The problem is in these two pictures, please show me the source code~

Answer 1

#include <iostream>

#include <math.h>

#include<fstream>

 

// function to calculate the factorial

int factorial(int n)

{

int fact = 1;

for (int i = 2; i <= n; i++)

fact *= i;   

return fact;

}

 

 

   

// fuction to calculate sum of the series

void series(int a, float b, int n)

{ float sum = 0;

for(int i = 0; i< n+1; i++){

int numfact = factorial(n); // calculates numerator n!

int denfact = factorial(n - i); //calculates denominator of ncr (n-i)!

int intfact = factorial(i); //calculates denominator of ncr i!

float ncr = numfact/(denfact * intfact); //final value of ncr

   

float A = pow(a,(n-1)); // calculates a term of binomial theorem

float B = pow(b,i); // calculates b term of binomial theorem

 

float mult = ncr*A*B; //represnts every single term of the binomial series

   

sum+= mult; //final sum

}

std::cout<<"(a+b)^n from binomial theorem: "<< sum <<"\n";

}

 

//function gets number from the file

void getNumber(float& num, std::istream& inf)

{

inf >> num;

}

 

 

//main function

int main() {

int m; //value of m from the file

int a = 1;

float b;

float n;

 

std::ifstream inf;

inf.open("BINO.DAT");

inf >> m; //value of m is recorded

for(int i = 0; i<2*m; i++){

getNumber(b ,inf); //value of b is recorded here

i++;

getNumber(n, inf); //value of n is recorded here

series(a,b,n); //represents binomial answer

std::cout<<"(a+b)^n from pow() function: "<<pow(a+b,n)<<"\n\n"; //represents pow() function answer

}

}