Question

Write a C++ program that computes the following series:

sum = 1/firstPrime + 2/secondPrime+…..+1/n^thPrime

Your program should prompt the user to enter a number n. The program will compute and display sum based on the series defined above.

firstPrime: is 2

secondPrime: the first prime number after 2

thirdPrime: the third prime number

….

n^th prime: the n^th prime number

Your program must be organized as follows:

int main() {

//prompt the user to enter n

//read n from the user

//compute series

//print result

return 0;

}

bool isPrime(int num) {

// if num is prime return true

//else return false

}

Answer 1

In the question you have written sum as sum = 1/firstPrime + 2/secondPrime+…..+1/n^thPrime

I think it should be

sum = 1/firstPrime + 2/secondPrime+…..+n/n^thPrime  where each term represents (n/nth prime)

or  sum = 1/firstPrime + 1/secondPrime+…..+1/n^thPrime where each term represents (1/nth prime)

i have written code for both, you just have to comment the line depending on which you want.

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I have included my code and screenshots in this answer. In case, there is any indentation issue due to editor, then please refer to code screenshots to avoid confusion.

--------------------main.cpp-------------------

#include <iostream>
#include <string.h>
using namespace std;

bool isPrime(int num);

int main()
{
   int n;
   cout << "\n Enter the value of n: ";
   cin >> n;
   cout << "\n sum is ";
   double sum = 0;

   int prime_count = 0; //to count number of primes found so far
   int num = 1; //number to be checked for prime
   while(prime_count < n)
   {
       if(isPrime(num)) //check if number is prime, if not prime move to next number
       {
           prime_count++; //if prime num then increment prime_count
           sum = sum + prime_count/(double)num; //Series: 1/p1 + 2/p2 + 3/p3 + ... + n/pn
           if(prime_count < n)
               cout << prime_count << "/" << num << " + ";
           else
               cout << prime_count << "/" << num << " = ";
           /*sum = sum + 1/(double)num; //if Series: 1/p1 + 1/p2 + 1/p3 + ... + 1/pn
           if(prime_count < n)
               cout << 1 << "/" << num << " + ";
           else
               cout << 1 << "/" << num << " = "; */
       }
       num++; //move to next number
   }
   cout << sum << endl;
   return 0;
}

bool isPrime(int num){ //checks if an input number is prime
   if(num < 2) //if num is less than 2 it is not prime
       return false;

   for(int i = 2; i <= num/2; i++){ //check if number is divided by any smaller number
       if(num % i == 0) //if any number divides then num is not prime
           return false;
   }
   return true; //if no number divides, then number is prime
}

--------------------Screenshots main.cpp-------------------

/cpp/temp/main.cpp - Sublime Text (UNREGISTERED) ti 1) 5:44 AM * main.cpp X #include <iostream> #include <string.h> using namespace std; bool isPrime(int num); int main() { 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 int n; cout << "\n Enter the value of n: "; cin >> n; cout << "\n sum is "; double sum = 0; 18 { 19 20 { A 21 22 23 24 25 int prime_count = 0; //to count number of primes found so far int num = 1; //number to be checked for prime while(prime_count <n) if(isPrime(num)) //check if number is prime, if not prime move to next number prime_count++; //if prime num then increment prime_count sum = sum + prime count/(double)num; //Series: 1/p1 + 2/p2 + 3/p3 + ... + n/pn if(prime_count < n) cout << prime_count << "/" « num << " + "; else cout << prime_count << "/" << num << " = "; /*sum = sum + 1/(double) num; //if Series: 1/pl + 1/p2 + 1/p3 + ... + 1/pn if(prime_count < n) cout << 1 << "/" << num << " + "; else cout << 1 « "/" << num << " = "; */ num++; //move to next number } cout << sum << endl; return 0; 26 27 28 29 30 31 } } 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 bool isPrime(int num) { // checks if an input number is prime if(num < 2) //if num is less than 2 it is not prime return false; for(int i = 2; i <= num/2; i++){ //check if number is divided by any smaller number if(num $i == 0) //if any number divides then num is not prime return false; return true; //if no number divides, then number is prime } یا Line 48, Column 2; Saved -/cpp/temp/main.cpp (UTF-8) Tab Size: 4 C++

--------------------Output-------------------

5:45 AM vs@ubuntu:-/pp/temp vs@ubuntu:-/cpp/temp$ 9++ main.cpp vs@ubuntu:-/cpp/temp$ ./a.out Enter the value of n: 10 sum is 1/2 + 2/3 + 3/5 + 4/7 + 5/11 + 6/13 + 7/17 + 8/19 + 9/23 + 10/29 = 4.82313 vs@ubuntu:-/cpp/temp$ ./a.out Enter the value of n: 20 sum is 1/2 + 2/3 + 3/5 + 4/7 + 5/11 + 6/13 + 7/17 + 8/19 + 9/23 + 10/29 + 11/31 + 12/37 + 13/41 + 14/43 + 15/47 + 16/53 + 17/59 + 18/61 + 19/67 + 20/71 = 7.91447 vs@ubuntu:-/cpp/temp$ g++ main.cpp vs@ubuntu:-/cpp/temp$ ./a.out Enter the value of n: 25 sum is 1/2 + 2/3 + 3/5 + 4/7 + 5/11 + 6/13 + 7/17 + 8/19 + 9/23 + 10/29 + 11/31 + 12/37 + 13/41 + 14/43 + 15/47 + 16/53 + 17/59 + 18/61 + 19/67 + 20/71 + 21/73 + 22/79 + 23/83 + 24/89 + 25/97 = 9.28513 vs@ubuntu:-/cpp/temp$ ./a.out C Enter the value of n: 60 sum is 1/2 + 2/3 + 3/5 + 4/7 + 5/11 + 6/13 + 7/17 + 8/19 + 9/23 + 10/29 + 11/31 + 12/37 + 13/41 + 14/43 + 15/47 + 16/53 + 17/59 + 18/61 + 19/67 + 20/71 + 21/73 + 22/79 + 23/83 + 24/89 + 25/97 + 26/101 + 27/103 + 28/107 + 29/109 + 30/113 + 31/127 + 32/131 + 33/137 + 34/139 + 35/149 + 36/151 + 37/157 + 38/163 + 39/167 + 40/173 + 41/179 + 42/181 + 43/191 + 44/193 + 45 /197 + 46/199 + 47/211 + 48/223 + 49/227 + 50/229 + 51/233 + 52/239 + 53/241 + 54/251 + 55/257 + 56/263 + 57/269 + 58/271 + 59/277 + 60/281 = 17.3755 vs@ubuntu:-/cpp/temps |

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I hope this helps you,

Please rate this answer if it helped you,

Thanks for the opportunity