The sum of n natural numbers formula helps you quickly calculate the total of the first n counting numbers without adding each value manually. This is especially useful in arithmetic, algebra, competitive exams, and real-life situations where fast calculation is needed. The formula shows a clear numerical pattern that appears when we arrange natural numbers in a sequence. Once you know the value of n, finding the sum becomes effortless.
Sum of n Natural Numbers Formula Overview
| Formula | Variables | When It Is Used |
|---|---|---|
| S = n(n + 1) / 2 | S = sum of numbers | To find the total quickly |
| n = number of terms | Used in sequences & series |
What is the Sum of n Natural Numbers in Maths?
Natural numbers are positive counting numbers starting from 1. Examples include 1, 2, 3, 4, 5, and so on. These numbers play an important role in arithmetic, algebra, patterns, and number theory.
The formula S = n(n + 1)/2 helps you add the first n natural numbers without writing the entire sequence. Instead of adding numbers like 1 + 2 + 3 + … + n individually, the formula uses a simple pattern that gives the result in seconds.
How the Formula Works
- Identify how many natural numbers (n) are given.
- Substitute the value of n into the formula.
- Simplify and get the total.
This formula is frequently used in competitive exams like CUET, SSC, Banking, JEE, and also in real-life counting tasks such as estimating items, seats, or arrangements.
Examples to Calculate Sum of n Natural Numbers
Example 1: Sum of First 10 Natural Numbers
Step 1: n = 10
Step 2: S = 10(10 + 1)/2
Step 3: S = 10 × 11 / 2 = 55
So, the sum of the first 10 natural numbers is 55.
Example 2: Sum of First 50 Natural Numbers
Step 1: n = 50
Step 2: S = 50(50 + 1)/2
Step 3: = (50 × 51) / 2 = 1275
So, the sum of the first 50 natural numbers is 1275.
FAQs about Sum of n Natural Numbers Formula
Q1. What is the sum of the first 100 natural numbers?
Using S = n(n + 1)/2,
S = 100(100 + 1)/2 = 5050.
Q2. Can we use this formula for large numbers?
Yes, it works for any positive integer n, even very large values.
Q3. Is 0 included in natural numbers?
Traditionally no, natural numbers begin with 1. Some modern definitions include 0.
Q4. Where is this formula used in exams?
It appears in AP (Arithmetic Progression), number theory, and aptitude problems in CUET, SSC, Banking, JEE, Railways, and school exams.
Q5. What is the difference between natural and whole numbers?
Natural numbers start at 1. Whole numbers start at 0.
Q6. Who discovered this formula?
It is commonly credited to the mathematician Carl Friedrich Gauss, who identified the pattern as a child.