The sum of the first 100 counting numbers (1 to 100) is 5050.
Calculating the Sum
We can calculate the sum of the first 100 counting numbers using a formula. According to the provided reference, the formula for the sum of natural numbers is:
S = n/2 [2a + (n − 1) × d]
Where:
- S = Sum of the numbers
- n = Number of terms (in this case, 100)
- a = First term (in this case, 1)
- d = Common difference (in this case, 1)
Applying these values, we get:
S = 100/2 [2(1) + (100 - 1) × 1]
S = 50 [2 + 99]
S = 50 [101]
S = 5050
Formula Application
The formula used is a generalized version for arithmetic series, but a simplified formula exists specifically for the sum of the first 'n' natural numbers:
S = n(n+1)/2
For n = 100:
S = 100(100+1)/2
S = 100(101)/2
S = 10100/2
S = 5050
Example
Let's illustrate the concept with a smaller set. What is the sum of the first 10 counting numbers?
- n = 10
S = 10(10+1)/2
S = 10(11)/2
S = 110/2
S = 55
Therefore, 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
Summary
| Detail | Value |
|---|---|
| Sum of first 100 numbers | 5050 |
| Formula Used | S = n(n+1)/2 |
| Number of terms (n) | 100 |
