L3.6: for loop to add the first n numbers

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Learning outcomes

• sum first n numbers using for
• verify result using formula n(n+1)/2
• write variants (even/odd sums)

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Basic solution

n = int(input())
total = 0
for i in range(1, n + 1):
    total += i
print(total)

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Dry run for n = 4

• total = 0
• add 1 -> 1
• add 2 -> 3
• add 3 -> 6
• add 4 -> 10

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Formula cross-check

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Variant 1: sum of even numbers up to n

n = int(input())
total = 0
for i in range(2, n + 1, 2):
    total += i
print(total)

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Variant 2: sum of odd numbers up to n

n = int(input())
total = 0
for i in range(1, n + 1, 2):
    total += i
print(total)

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Exam hints and traps

• inclusive range needs n + 1
• range(n) starts from 0, not 1
• for large n, formula is faster than loop

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Practice

1. Write loop sum for first n natural numbers.
2. Modify to sum from a to b inclusive.
3. Predict output for n=0.

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Answers

total = 0
for i in range(a, b + 1):
    total += i

3. 0