PREVIOUSLY ASKED IN:
WBPSC Miscellaneous Preliminary 2023
Answer
5050
Explanation
The sum of the first \( n \) natural numbers can be calculated using the formula \( S = \frac{n(n+1)}{2} \). Here, the value of \( n \) is 100. Plugging this into the formula gives: \( \frac{100 \times 101}{2} = 50 \times 101 = 5050 \). This is a classic example of finding the sum of an arithmetic progression.
Key Points
- > Sum of natural numbers formula: \( \frac{n(n+1)}{2} \).
- > Sum of first 'n' even numbers: \( n(n+1) \).
- > Sum of first 'n' odd numbers: \( n^2 \).
- > Arithmetic Progression sum: \( S_n = \frac{n}{2}[2a + (n-1)d] \).
- > The average of numbers from 1 to 100 is \( 50.5 \).
- > Carl Friedrich Gauss famously solved this problem quickly as a schoolboy.
- > Sum of squares: \( \frac{n(n+1)(2n+1)}{6} \).
Additional Information
Mathematical Series Formulas
| Sequence | Formula | Example (n=10) |
|---|---|---|
| Natural Numbers | \( \frac{n(n+1)}{2} \) | \( 55 \) |
| Odd Numbers | \( n^2 \) | \( 100 \) |
| Even Numbers | \( n(n+1) \) | \( 110 \) |
Memory Tips
- Double Fifty: The sum of 1 to 100 is simply the number 50 written twice (5050).