What is the first term when applying binomial theorem

1

Step-by-step explanation:

Binomial theorem is describing the expansion of powers of the term (a + b)^n

Obviously if n = 0, a + b = 1

So the first term is 1.

/ Sierpinski.java

public class Sierpinski {

     // method to find the height of an equilateral triangle with side length =

     // length

     public static double height(double length) {

           // formula= length*sqrt(3)/2

           double h = (length * Math.sqrt(3)) / 2.0;

           return h;

     }

     // method to draw a filled triangle (pointed downwards) with bottom vertex

     // x,y

     public static void filledTriangle(double x, double y, double length) {

           // finding height

           double h = height(length);

           // filling triangle as a polygon

           // passing x, x-length/2, x+length/2 as x coordinates

           // and y, y+h, y+h as y coordinates

           StdDraw.filledPolygon(new double[] { x, x - (length / 2.0),

                       x + (length / 2.0) }, new double[] { y, y + h, y + h });

     }

     // method to draw an n level sierpinski triangle

     public static void sierpinski(int n, double x, double y, double length) {

           // checking if n is above 0 (base condition)

           if (n > 0) {

                 // drawing a filled triangle with x, y as bottom coordinate, length

                 // as side length

                 filledTriangle(x, y, length);

                 // drawing the triangle(s) on the top

                 sierpinski(n - 1, x, y + height(length), length / 2);

                 // drawing the triangle(s) on the left side

                 sierpinski(n - 1, x - (length / 2.0), y, length / 2);

                 // drawing the triangle(s) on the right side

                 sierpinski(n - 1, x + (length / 2.0), y, length / 2);

           }

     }

     public static void main(String[] args) {

           // parsing first command line argument as integer, if you dont provide

           // the value while running the program, this program will cause

           // exception.

           int n = Integer.parseInt(args[0]);

           // length of the outline triangle

           double length = 1;

           // finding height

           double h = height(length);

           // drawing a triangle (pointed upwards) to represent the outline.

           StdDraw.polygon(new double[] { 0, length / 2, length }, new double[] {

                       0, h, 0 });

           // drawing n level sierpinski triangle(s) with length / 2, 0 as x,y

           // coordinates and length / 2 as initial side length

           sierpinski(n, length / 2, 0, length / 2);

     }

}