Triangle Numbers

The n-th triangle number is the sum of all integers from 1 to n:

tri(n) = 1 + 2 + 3 + ... + n

Notice that this is the number of bricks it takes to build a triangular staircase of height n:

Here's a nice shortcut to compute tri(n) that doesn't require iteration or recursion:

tri(n)

= 1 + 2 + 3 + ... + n

= (n + 1) + (n – 1 + 2) + ... (n – (n/2 – 1) + n/2)

= (n + 1) + (n + 1) + ... + (n + 1)

= (n + 1) * n/2

Here's an implementation in Java:

class Triangle {
public int tri(int n) {
return (n + 1) * n/2;
}
}

A test harness can be found in TestTriangle.java.

Translate the definition of class Triangle into Jasmin. Save your definition in a file called Triangle.j. Assemble it and test it using TestTriangle.