1 + 2 + 3 + 4 + 5 + 6 To 100

2 min read Jun 17, 2024
1 + 2 + 3 + 4 + 5 + 6 To 100

The Sum of the First 100 Natural Numbers

The sum of the first 100 natural numbers, represented as 1 + 2 + 3 + 4 + 5 + 6... + 100, is a classic mathematical problem with a simple and elegant solution.

Understanding the Pattern

Instead of adding each number individually, there's a clever way to visualize the sum:

  1. Pair the numbers: Pair the first and last number (1 + 100), the second and second-to-last (2 + 99), and so on.
  2. Equal sums: Notice that each pair adds up to the same value (101).
  3. Number of pairs: Since we have 100 numbers, we have 50 pairs.

The Formula

This leads to the formula:

(Sum of first 100 natural numbers) = (Number of pairs) * (Sum of each pair)

Therefore, the sum is: 50 * 101 = 5050

Generalizing the Solution

This method can be generalized for any sequence of consecutive natural numbers. The sum of the first 'n' natural numbers is:

(n/2) * (n + 1)

For example, to find the sum of the first 20 natural numbers:

(20/2) * (20 + 1) = 10 * 21 = 210

Conclusion

The sum of the first 100 natural numbers is 5050. This simple formula and the visualization of pairing numbers provide a clear and efficient way to calculate this sum, and it can be applied to any sequence of consecutive natural numbers.

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