To find the sum of the natural numbers up to 200, we can use a well-known formula that calculates the sum of the first [tex]\( n \)[/tex] natural numbers. This formula is:
[tex]\[ \text{Sum} = \frac{n(n + 1)}{2} \][/tex]
Here's a step-by-step breakdown of how to use this formula:
1. Identify the highest natural number, which in this case is [tex]\( n = 200 \)[/tex].
2. Plug [tex]\( n = 200 \)[/tex] into the formula:
[tex]\[ \text{Sum} = \frac{200 \times (200 + 1)}{2} \][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[ 200 + 1 = 201 \][/tex]
4. Now, substitute back into the formula:
[tex]\[ \text{Sum} = \frac{200 \times 201}{2} \][/tex]
5. Perform the multiplication:
[tex]\[ 200 \times 201 = 40200 \][/tex]
6. Finally, divide by 2:
[tex]\[ \frac{40200}{2} = 20100 \][/tex]
Therefore, the sum of the natural numbers up to 200 is [tex]\( 20100 \)[/tex].
