FAQ: Induction and Strong Induction - Induction: Induction Hypothesis

Frequently Asked Questions Uncategorized
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This community-built FAQ covers the “Induction: Induction Hypothesis” exercise from the lesson “Induction and Strong Induction”.

Paths and Courses
This exercise can be found in the following Codecademy content:

[Beta] Discrete Math

FAQs on the exercise Induction: Induction Hypothesis

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for i in range(1, k + 1):
s += 2 * i - 1

why do use “k+1” for the end range, why not just k ?

3

In Python, range returns a sequence of numbers in which the starting number is included but the stop/end number is not included.

For Example,

print(list(range(1, 5)))
# [1, 2, 3, 4]
# 1 is included but 5 is not included

print(list(range(4, 7)))
# [4, 5, 6]
# 4 is included but 7 is not included

print(list(range(3, 11, 2)))  
# [3, 5, 7, 9] (Step size of 2)
# 3 is included but 11 is not included

In the exercise, it is specified:

… set s to store the sum of first i odd integers, where i is a value starting at 1 and increments each iteration until the first k odd integers have been added together

Since we want to sum the first k odd integers, so we should specify k + 1 as the stop for the range,

# This is what we want
range(1, k + 1)
# 1, 2, 3, ... , k - 1, k

# This is not what we want
range(1, k)
# 1, 2, 3, ... , k - 1