what a solution 1+2+3+... +198+199+200=?  show your solution

To solve the sum \(1 + 2 + 3 + \dots + 198 + 199 + 200\), we can use the formula for the sum of the first \(n\) natural numbers:

\[
S_n = \frac{n(n+1)}{2}
\]

In this problem, \(n = 200\), so we can substitute \(n = 200\) into the formula:

\[
S_{200} = \frac{200 \times (200 + 1)}{2}
\]

Simplifying this:

\[
S_{200} = \frac{200 \times 201}{2} = \frac{40200}{2} = 20100
\]

Thus, the sum \(1 + 2 + 3 + \dots + 198 + 199 + 200\) is \( \boxed{20100} \).

Would you like more details or have any questions?

Here are 8 related questions for further exploration:
1. What is the sum of the first 100 natural numbers?
2. How would you find the sum of all even numbers from 2 to 200?
3. Can you prove the formula \( S_n = \frac{n(n+1)}{2} \) using induction?
4. What is the sum of the first 200 odd numbers?
5. How would you calculate the sum of squares of the first 200 natural numbers?
6. How does the sum formula change if the sequence starts from a number other than 1?
7. What is the sum of the first \( n \) multiples of a given number?
8. How would you approach finding the sum \(1 + 2 + 3 + \dots + 999\)?

**Tip:** For large sums or sequences, look for patterns or use known formulas to simplify calculations.

Learn how to calculate the sum of the first 200 natural numbers with a detailed step-by-step solution. This problem covers key arithmetic concepts, including the formula for the sum of natural numbers. Suitable for students in Grades 7-9.

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