Very easy question

1 + 2 + 3 + 4 + … + 98 + 99 + 100

I noticed that if he was to split the numbers into two groups
Like (1 to 50 and 51 to 100)
I could add them together vertically to get a sum of 101.
1 + 2 + 3 + 4 + 5 + … + 48 + 49 + 50

100 + 99 + 98 + 97 + 96 + … + 53 + 52 + 51

1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
.
.
.
48 + 53 = 101
49 + 52 = 101
50 + 51 = 101

I realized then that his final total would be 50(101) = 5050.

The sequence of numbers (1, 2, 3, … , 100) is arithmetic and when we are looking for the sum of a sequence, we call it a series. Thanks to Gauss, there is a special formula we can use to find the sum of a series:
S=n(n+1)/2
S is the sum of the series and n is the number of terms in the series, in this case, 100.
S=100(100+1)/2

Hope this helps!

There are other ways to solve this problem. You can, for example, memorize the formula

This is an arithmetic series, for which the formula is:
S = n[2a+(n-1)d]/2
where a is the first term, d is the difference between terms, and n is the number of terms.
For the sum of the first 100 whole numbers:
a = 1, d = 1, and n = 100
Therefore, sub into the formula:
S = 100[2(1)+(100-1)(1)]/2 = 100[101]/2 = 5050

**Finding the Sum of the First 100 Natural Numbers Without Using the Sum Formula**

To find the sum of the first 100 natural numbers without using the sum formula, we can apply a simple mathematical approach. Let's break down the process into steps:

**Step 1: Understand the Problem**
- We are required to find the sum of the first 100 natural numbers.
- Natural numbers are positive integers starting from 1.

**Step 2: Define Variables**
- We can define a variable "sum" to keep track of the running sum as we add each natural number.
- Initialize the variable "sum" to zero.

**Step 3: Loop Through the Natural Numbers**
- We will use a loop to iterate through the first 100 natural numbers.
- Starting from 1, we will keep adding each number to the "sum" variable.

**Step 4: Calculate the Sum**
- After adding all the numbers from 1 to 100, we will have the sum of the first 100 natural numbers stored in the "sum" variable.

**Step 5: Display the Result**
- Finally, we can display the value of the "sum" variable, which will be the sum of the first 100 natural numbers.

**Code Implementation in Python:**
```python
# Step 2: Define Variables
sum = 0

# Step 3: Loop Through the Natural Numbers
for i in range(1, 101):
# Step 4: Calculate the Sum
sum += i

# Step 5: Display the Result
print("The sum of the first 100 natural numbers is:", sum)
```

**Explanation of the Code:**
- In this Python code, we start by initializing the "sum" variable to zero.
- We then use a for loop to iterate through the range of numbers from 1 to 100 (both inclusive).
- Inside the loop, we add each number to the "sum" variable using the "+=" operator, which updates the value of "sum" by adding the current number.
- After the loop completes, the "sum" variable will hold the sum of the first 100 natural numbers.
- Finally, we print the value of the "sum" variable, which gives us the desired result.

**Conclusion:**
By following the steps mentioned above and implementing the code in Python, we can find the sum of the first 100 natural numbers without using the sum formula. The code is based on a simple iterative approach, where we add each natural number to a running sum variable.