# Sum the integers from 1 to n in Python

Last updated: Jul 4, 2022

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## Sum the integers from 1 to n in Python#

Multiply by n + 1 and floor-divide by `2` to get the integers from 1 to n, e.g. `total = n * (n + 1) // 2`. The result will be the sum of the integers from 1 to n (including n).

main.py
```Copied!```n = 5

total = n * (n + 1) // 2
print(total)  # 👉️ 15

# --------------------------------

total_2 = sum(range(1, n + 1))
print(total_2)  # 👉️ 15

# 👇️ [1, 2, 3, 4, 5]
print(list(range(1, n + 1)))
``````

The first example multiplies `n` by `n + 1` and floor-divides by `2` to get the sum of the integers from `1` to `n`.

Division `/` of integers yields a float, while floor division `//` of integers result in an integer.

The result of using the floor division operator is that of a mathematical division with the `floor()` function applied to the result.

If you don't want to use a formula, use the `range()` class.

To sum the integers from 1 to n:

1. Pass `1` and `n+1` to the `range` class, e.g. `range(1, n + 1)`.
2. Pass the `range` object to the `sum()` function.
3. The `sum` function will sum the integers from 1 to `n`.
main.py
```Copied!```n = 5

total_2 = sum(range(1, n + 1))
print(total_2)  # 👉️ 15

# 👇️ [1, 2, 3, 4, 5]
print(list(range(1, n + 1)))
``````

We used the `range()` class to sum the numbers from 1 to `n`.

The range class is commonly used for looping a specific number of times in `for` loops and takes the following arguments:

NameDescription
`start`An integer representing the start of the range (defaults to `0`)
`stop`Go up to, but not including the provided integer
`step`Range will consist of every N numbers from `start` to `stop` (defaults to `1`)
Notice that we added `1` to the `stop` value. The `stop` argument is exclusive, so we had to add `1` to include `n` in the result.

If you only pass a single argument to the `range()` constructor, it is considered to be the value for the `stop` parameter.

main.py
```Copied!```n = 5

total_2 = sum(range(n + 1))
print(total_2)  # 👉️ 15

# 👇️ [0, 1, 2, 3, 4, 5]
print(list(range(n + 1)))
``````
The example shows that if the `start` argument is omitted, it defaults to `0` and if the `step` argument is omitted, it defaults to `1`.

Since the `start` argument of the range is `0`, you can omit it and you'd get the same result.

If values for the `start` and `stop` parameters are provided, the `start` value is inclusive, whereas the `stop` value is exclusive.

If the value for the `stop` parameter is lower than the value for the `start` parameter, the range will be empty.

main.py
```Copied!```# 👇️ []
print(list(range(5, 1)))

total = sum(range(5, 1))
print(total)  # 👉️ 0
``````

The `sum` function can be used to calculate the sum of the numbers in the range.

The sum function takes an iterable, sums its items from left to right and returns the total.

The `sum` function takes the following 2 arguments:

NameDescription
iterablethe iterable whose items to sum
startsums the `start` value and the items of the iterable. `sum` defaults to `0` (optional)

If you need to get a range with a step, pass a value for the third argument of the `range()` class.

main.py
```Copied!```start = 1
stop = 5
step = 2

total_2 = sum(range(start, stop + 1, step))

print(total_2)  # 👉️ 9 (1 + 3 + 5)

# 👇️ [1, 3, 5]
print(list(range(start, stop + 1, step)))
``````

When the `step` argument is provided, the range will consist of every N numbers from `start` to `stop`.

The value for the `step` argument defaults to `1`.

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