How to avoid updating the file content at each run
#include <iostream>
#include <fstream>
#include <math>
using namespace std;
int main() {
  ofstream file("file.txt");
  v2 = rand() % 100 + 1;
  file<< v2;
  file.close();
  return 0 ;
}
I am looking to add a new line at each run containing the new random value and conserving the old one wrote during the previous run .
                        
You need to specify the "append" mode when opening the file:
See http://en.cppreference.com/w/cpp/io/basic_ofstream/basic_ofstream and http://en.cppreference.com/w/cpp/io/ios_base/openmode for details. Opening a file for output, without specifying the open mode, will by default truncate the file.