1. Compute and print both roots of the quadratic equation x^2 – 5.86 x + 8.5408.

Use a for loop to print the decimal representations of 1/2, 1/3, ..., 1/10, one on each line.

2. Use a for loop to compute the 10th triangular number. The nth triangular number is defined as

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

(You can also compute the nth triangular number as n*(n+1)/2. Use this formula to doublecheck that your loop is correct.)

Hint: This outline is an almost-complete solution. You only must replace each ellipsis by an

expression.

3. Use a for loop to compute 10! (the factorial of 10). Recall that the factorial of n is 1*2*3*...*n.

The first line of your solution will be n = 10. After that, your solution should not use 10 again,

though your solution will use n. In other words, your code (after the n = 10 line) should work for

any value of n.

Hint: Your answer will be like your answer to "Problem 3: Triangular numbers".

4. Write code to print the first 10 factorials, in reverse order. In other words, write code that prints

10!, then prints 9!, then prints 8!, ..., then prints 1!. Its literal output will be:

3628800

362880

40320

5040

720

120

24

621

The first line of your solution should assign a variable numlines to 10, and then the rest of your

solution must not use 10 anywhere.

Hint: Use two nested for loops.

5. Compute the following value:

1 + 1/1! + 1/2! + 1/3! + 1/4! + ... + 1/10!

The value should be close to e (≈ 2.71828), the base of the natural logarithms.

Hint: The easiest way to solve this is with two nested for loops. It is possible, but tricky, to

compute this using only one for loop. That is not necessary for this assignment.

Hint: Copy your solution to "Problem 5: Multiple factorials", then modify it. Rather than printing

the factorials, you will add their reciprocals to a running total, then print that total at the end.

Hint: don't try to work the very first "1 +" into your loop; do it outside the loops (either at the

very beginning or the very end of the outer loop).

6. Compute the following value: 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... + 1/10!

The value should be close to e (≈ 2.71828), the base of the natural logarithms.

Hint 1: The easiest way to solve this is with two nested for loops. It is possible, but tricky, to

compute this using only one for loop. That is not necessary for this assignment.

Hint: Copy your solution to "Problem 5: Multiple factorials", then modify it. Rather than printing

the factorials, you will add their reciprocals to a running total, then print that total at the end.

Hint: don't try to work the very first "1 +" into your loop; do it outside the loops (either at the

very beginning or the very end of the outer loop).

7. NOT GRADED: import the MS Excel Worksheet Sample_01 to Python. Do all sort of statistics and

graphs. Prepare a small database to import the values in Sample_01, like we have seen in

5_class_example.py.

GOOD LUCK!