A good answer might be:

Yes. The calculation gets rather tedious, but the definition works for all positive integers.

Java Method

It might be nice to have a Java method that does the calculation for us. Here is a math-like definition of Triangle(N):

  1. Triangle( 1 ) = 1
  2. Triangle( N ) = N + Triangle( N-1 )

And here is a Java method that does this calculation: 

int Triangle( int N )
{
  if ( N == 1 )
    return 1;
  else
    return N + Triangle( N-1 );
}

The Java code is similar to the math-like definition of Triangle(). The if statement has been added so that the base case is selected when it is needed.

QUESTION 8:

Is it OK to have Triangle( N-1 ) in the body of the method?