Programming

Formatting¶

For this homework, you will need to edit hw1.py so that when it runs, your answers are printed in the following format (replacing ____ with your answer):

Problem 1 solution follows:
Root 1: ____
Root 2: ____

Problem 2 solution follows:
1/2: ____
1/3: ____
1/4: ____
1/5: ____
1/6: ____
1/7: ____
1/8: ____
1/9: ____
1/10: ____

Problem 3 solution follows:
Triangular number 10 via loop: ____
Triangular number 10 via formula: ____

Problem 4 solution follows:
10!: ____

Problem 5 solution follows:
10!: ____
9!: ____
8!: ____
7!: ____
6!: ____
5!: ____
4!: ____
3!: ____
2!: ____
1!: ____

Problem 6 solution follows:
e: ____

Problem 1: Roots¶

Compute and print both roots in ascending order of the following quadratic equation:

$$3x^2-5.86x+2.5408$$

You will need to use the quadratic equation to solve for the roots:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Problem 2: Reciprocals¶

Use a for loop to print the decimal representations of the following fractions, each on their own line:

$$\frac{1}{2}, \frac{1}{3}, ..., \frac{1}{10}$$

Problem 3: Triangular Numbers¶

Use a for loop to compute the 10^th triangular number. The n^th triangular number is defined as 1+2+3+...+n, or by the formula:

$$\frac{n(n+1)}{2}$$

We have provided a partial solution to solve this problem in the starter code. Your solution should be able to correctly calculate the 11^th, 12^th, etc. triangular number by changing the variable n, for any number greater than 0.

Problem 4: Factorial¶

Use a for loop to compute 10!, the factorial of 10. The factorial of a number, n, can be calculated by

$$1 * 2 * 3 * ... * n$$

Similarly to problem 3, your solution should be able to correctly calculate any factorial just by changing a variable.

Problem 5: Multiple Factorials¶

Print the first 10 factorials in descending order (10!, 9!, …, 1!).

The first line of your solution should assign a variable num_lines to 10, and then the rest of your solution should print the correct number of lines and factorial on its own line. Similarly to problems 3 and 4, your solution should be able to work for any number just by changing num_lines.

The literal output for this problem will be:

10!: 3628800
9!: 362880
8!: 40320
7!: 5040
6!: 720
5!: 120
4!: 24
3!: 6
2!: 2
1!: 1

Problem 6: Sums of reciprocals of factorials¶

Use a for loop to compute the following value:

$$1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + ... + \frac{1}{10!}$$

Similar to problems 3 - 5, you should assign a variable (e.g., n = 10) to determine the number of fractions to add.

Code Quality¶

Your assignment should pass two checks: flake8 and our code quality guidelines. The code quality guidelines are very thorough. For this assignment, the most relevant rules can be found in these sections:

• Variable Names
• Whitespace
• Line Length
• Documentation

Submission¶

Submit hw1.py on Gradescope under the assignment Homework 1.