C++ program

The answer is 6.17103..., or precisely 15551/2520 if you want more precision for verifcation purposes.
The recursive method itself takes the header with one integer parameter and two statements, so it should be simple as you requested. The method sum is reproduced here, but for clarity you can view the function with the complete test program by clicking at this link.

double sum(int n)
{
if(n==1)return (double)1/2;
return sum(n-1)+(double)n/(n+1);
}