#include <iostream>
//where is my mistake?
using namespace std;

int main()
{
    int number, result;
    cout << "Enter number: " << endl;
    cin >> number;
    result = number;
    if (number > 0 && number <= 10000)
    {
        for (int i = 1; i<number; i++)
        {
            result = result + i;
        }
    }

    else if (number <= 0 && number >= -10000)
    {
        for (int j = 1; j > number; j--)
        {
            result = result + j;
        }
    }
    else
    {
        cout << "Enter the number within the limits of [-10000;10000]" << endl;
        return main();
    }
    cout << "Otvet: " << result << endl;
    return 0;
}

Edited by author 25.02.2013 22:28

You should not output any other text, only the solution.

You shound't cout any extral words!
For example : not  cout << "Enter number: " << endl;
and change cout << "Otvet: " << result << endl; tocout << result << endl;