Example

Here is our solution for triangle numbers:

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

Here is another example, calculating Triangle( 5 ):

Triangle( 5 ) = 5 +  Triangle( 4 )
              = 5 + ( 4 + Triangle( 3 ) )
              = 5 + ( 4 + ( 3 + Triangle( 2 ) ))
              = 5 + ( 4 + ( 3 + ( 2 + Triangle( 1 ) )))
              = 5 + ( 4 + ( 3 + ( 2 +      1        )))
              
              = 5 + ( 4 + ( 3 + 3) )
              = 5 + ( 4 + 6 )
              = 5 + 10
              = 15