Shortcut Trick for finding the sum of the first n natural numbers quickly.
This Superfast Technique is a shortcut trick for finding the sum of the first n natural numbers quickly.
General Formula: S = n(n+1)/2
where n is the last number.
Understanding the Trick (Superfast Method)
Rule:
- Divide the last number (n) by 2
- 2. Write the result twice (concatenate the digits)
Ex. 1: 1+2+3+...+10
· Step 1: 10/2=5
· Step 2: Write 5 twice → 55
· Answer: 55
Ex. 2: 1+2+3+...+100
· Step 1: 100/2=50
· Step 2: Write 50 twice → 5050
· Answer: 5050
Ex. 3: 1+2+3+...+1000
· Step 1: 1000/2=500
· Step 2: Write 500 twice → 500500
· Answer: 500500
Why Does It Work?
This trick is a shortcut for the standard formula: S = n(n+1)/2
For example:
Ex. 1. 1+2+3+...+10
Ans: 10(11) / 2 = 55
Ex. 2. 1+2+3+...+100
Ans: 100(101) / 2 = 5050
Ex. 3. 1+2+3+...+1000
Ans : 1000(1001) / 2 = 500500