Please program in C++ Program 4. Write a function: double zeta( double x) // her

Question

Please program in C++

Program 4. Write a function: double zeta( double x) // here x must be > 1.0 to compute and return the value of the sum Note that n is not a parameter of the function. Your while loop should stop adding once the term 1/k" becomes smaller than 10 parameter n and print the zeta value 10 Then in main function use a while loop to read values of the Program 5. Write a function int arithmeticsum( unsigned int a, unsigned int k, unsigned int n) to compute and return the value of the sum of the first n terms of an arithmetic sequence: a, a + k, a + 2k, . . . a + (n-1): where a and k are positive integers. The main function use a while loop to read values a, k, n and rint the sum with each iteration Program 6. Using the function: bool isprime( unsigned int n ) write a program to construct a vector of the first n prime numbers. Your program should 1. read in 2. use a while loop starting with 2 and with each iteration going up by one. 3. if a number is prime, add it to the vector; 4. finish the loop once n primes have been added. 5. Print the vector in the following fashion: supposing that n -10 your code should print primes[10]-2, 3, 5, 7, 11, 13, 17, 19, 23, 29)

Explanation / Answer

4)
/**
The c++ program that demonstrates the zeta
method.
*/
#include<iostream>
using namespace std;
//prototype zeta
double zeta(double x);
int main()
{

/**
The c++ program that demonstrates the zeta
method.
*/
#include<iostream>
using namespace std;
//prototype zeta
double zeta(double x);
int main()
{

   //call zeta method
   cout<<"zeta(2) :"
       <<zeta(2)<<endl;

   system("pause");
   return 0;
}
/*
Method zeta that takes double x
and returns zeta value.
*/
double zeta(double x)
{
   //set sum=0
   double sum=0;
   //set 10^-10=0.0000000001
   const double LIMIT=0.0000000001;
   double k=1;
   //run while loop until 1/k^x is >= LIMIT
   while((1/pow(k,x))>=LIMIT)
   {
       sum+=(1/pow(k,x));
       k=k+1;
   }
   //return sum
   return sum;
}

Sample output:

zeta(2): 1.64492

------------------------------------------------------------------------------

5)
/**
The c++ program that demonstrates the arithmeticsum
method.
*/
#include<iostream>
using namespace std;
//prototype arithmeticsum
int arithmeticsum(unsigned int a, unsigned int k, unsigned int n);
int main()
{

   //set a,k and n values
   unsigned int a=1;
   unsigned int k=10;
   unsigned int n=10;

   cout<<"a= "<<a<<endl;
   cout<<"k= "<<k<<endl;
   cout<<"n= "<<n<<endl;

   //calling arithmeticsum method
   cout<<"arithmeticsum(1,10,10) : "<<arithmeticsum(a,k,n)<<endl;

   system("pause");
   return 0;
}
/*
Method zeta that takes double x
and returns arithmeticsumvalue.
*/
int arithmeticsum(unsigned int a, unsigned int k, unsigned int n)
{
   //set sum=0
   double sum=0;
   int x=0;
   while(x<n-1)
   {
       sum+=(a+x*k);
       x=x+1;
   }
   //return sum
   return sum;
}

Sample output :
a= 1
k= 10
n= 10
arithmeticsum(1,10,10) : 369

------------------------------------------------------------------------------------
6)
/**
The c++ program that demonstrates the isprime
method.
*/
#include<iostream>
#include<vector>
using namespace std;
//prototype isprime
bool isprime(unsigned int n);
int main()
{
   //create a vector of integer type
   vector<int> primes;

   int x=2;
   int n=10;
   int primcount=0;
   //continue for 10 prime numbers
   while(primcount<n)
   {
       //check if start number is prime
       if(isprime(x))
       {
           primes.push_back(x);
           primcount++;
       }
       x++;
   }

   cout<<"primes["<<n<<"] = {";
   for (int i = 0; i < primes.size(); i++)
   {
       if(i==primes.size()-1)
           cout << primes[i]<< " ";
       else
       cout << primes[i]<< ",";
   }
   cout << "}";

   system("pause");
   return 0;
}
/*Returns true if the number n is prime */
bool isprime(unsigned int n)
{
   bool flag=true;
   for(int i = 2; i <= n / 2; i++)
   {
       if(n % i == 0) {
           flag = false;
           break;
       }
   }
   return flag;
}

Sample output:
primes[10] = {2,3,5,7,11,13,17,19,23,29 }

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