06 - L Advanced.md

✨ L Advanced ✨

Given a positive integer n, use a loop to store the sum of the reciprocals of the squares of the first n natural numbers in a float variable called sum:

Let's say the value of n is 4, then the sum would be:

This series is part of the Basel Problem. The infinite sum gives us .

How many times is statement executed when the following code is run?

for (int i = 0; i < 5; i++) {
    for (int j = 0; j < i; j+=2) {
        statement
    }
}

Recreate the following pattern using nested loops:

Note: the pattern provided is for n = 5. Your code should work for values of n between 1 and, say, 0.

1
2 1
3 2 1
4 3 2 1
5 4 3 2 1

Recreate the following pattern using nested loops:

Note: the pattern provided is for n = 4 (hence, 4 lines). Your code should work for values of n between 1 and, say, 20.

      1
    1 2 3
  1 2 3 4 5 
1 2 3 4 5 6 7

Use a nested loop to create the following image:

Recreate the following image using a loop:

HINT: The circles are along the circumference of a bigger circle, just at different angles.

Recreate the following image using a nested loop:

In the image above screen size of 400 by 400 pixels has been used. Additionally, the circles are offset by its radius.

How many times is statement executed when the following code is run?

for (int i = 15; i > 0; i-=5) {
    for (int k = 1; k < i; k += 3) {
        statement
    }
}

There is an error in the following code. Identify and correct the error.

for (int x = 20; x < width; x = x + 40)
{
	for (int y = 20; y <= x; y = y + 40)
	{
		circle(x, y, 10);
		circle(x, y - height, 10);
	}
}

The program is meant to produce the following image:

however, it is instead producing the following instead.

Find & correct for the error.