#### problem1 (Score: 1.5 / 10.0)

1. Test cell (Score: 0.0 / 1.0)
2. Test cell (Score: 1.0 / 1.0)
3. Test cell (Score: 0.0 / 0.5)
4. Test cell (Score: 0.5 / 0.5)
5. Written response (Score: 0.0 / 1.0)
6. Coding free-response (Score: 0.0 / 2.0)
7. Comment
8. Task (Score: 0.0 / 4.0)

Before you turn this problem in, make sure everything runs as expected. First, restart the kernel (in the menubar, select Kernel$\rightarrow$Restart) and then run all cells (in the menubar, select Cell$\rightarrow$Run All).

Make sure you fill in any place that says YOUR CODE HERE or "YOUR ANSWER HERE", as well as your name and collaborators below:

In [1]:
NAME = "Ben Bitdiddle"
COLLABORATORS = "Alyssa P. Hacker"


For this problem set, we'll be using the Jupyter notebook:

## Part A (2 points)¶

Write a function that returns a list of numbers, such that $x_i=i^2$, for $1\leq i \leq n$. Make sure it handles the case where $n<1$ by raising a ValueError.

In [2]:
def squares(n):
"""Compute the squares of numbers from 1 to n, such that the
ith element of the returned list equals i^2.

"""
if n < 1:
raise ValueError
s = []
for i in range(n):
s.append(i**2)
return s


Your function should print [1, 4, 9, 16, 25, 36, 49, 64, 81, 100] for $n=10$. Check that it does:

In [3]:
squares(10)

Out[3]:
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
In [4]:
Grade cell: correct_squares Score: 0.0 / 1.0 (Top)
"""Check that squares returns the correct output for several inputs"""
assert squares(1) == [1]
assert squares(2) == [1, 4]
assert squares(10) == [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
assert squares(11) == [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121]

---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-4-f3fef5b9ed4e> in <module>()
1 """Check that squares returns the correct output for several inputs"""
----> 2 assert squares(1) == [1]
3 assert squares(2) == [1, 4]
4 assert squares(10) == [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
5 assert squares(11) == [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121]

AssertionError: 
In [5]:
Grade cell: squares_invalid_input Score: 1.0 / 1.0 (Top)
"""Check that squares raises an error for invalid inputs"""
try:
squares(0)
except ValueError:
pass
else:
raise AssertionError("did not raise")

try:
squares(-4)
except ValueError:
pass
else:
raise AssertionError("did not raise")


## Part B (1 point)¶

Using your squares function, write a function that computes the sum of the squares of the numbers from 1 to $n$. Your function should call the squares function -- it should NOT reimplement its functionality.

In [6]:
def sum_of_squares(n):
"""Compute the sum of the squares of numbers from 1 to n."""
total = 0
s = squares(n)
for i in range(len(s)):
total += s[i]


The sum of squares from 1 to 10 should be 385. Verify that this is the answer you get:

In [7]:
sum_of_squares(10)

Out[7]:
285
In [8]:
Grade cell: correct_sum_of_squares Score: 0.0 / 0.5 (Top)
"""Check that sum_of_squares returns the correct answer for various inputs."""
assert sum_of_squares(1) == 1
assert sum_of_squares(2) == 5
assert sum_of_squares(10) == 385
assert sum_of_squares(11) == 506

---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-8-1a00eaa7c988> in <module>()
1 """Check that sum_of_squares returns the correct answer for various inputs."""
----> 2 assert sum_of_squares(1) == 1
3 assert sum_of_squares(2) == 5
4 assert sum_of_squares(10) == 385
5 assert sum_of_squares(11) == 506

AssertionError: 
In [9]:
Grade cell: sum_of_squares_uses_squares Score: 0.5 / 0.5 (Top)
"""Check that sum_of_squares relies on squares."""
orig_squares = squares
del squares
try:
sum_of_squares(1)
except NameError:
pass
else:
raise AssertionError("sum_of_squares does not use squares")
finally:
squares = orig_squares


## Part C (1 point)¶

Using LaTeX math notation, write out the equation that is implemented by your sum_of_squares function.

Student's answer Score: 0.0 / 1.0 (Top)

$\sum_{i=0}^n i^2$

## Part D (2 points)¶

Find a usecase for your sum_of_squares function and implement that usecase in the cell below.

In [10]:
Student's answer Score: 0.0 / 2.0 (Top)
# YOUR CODE HERE
raise NotImplementedError()

---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
<ipython-input-10-15b94d1fa268> in <module>()
NotImplementedError: 
$\sum x^i = \frac{1}{1-x}$