Comprehensive Calculator Guide
This calculator works out the nth triangular number, the sum of 1 to n, by n(n + 1) ÷ 2. The 10th is 55 and the sum of 1 to 100 is 5050. It explains Gauss’s pairing trick, the triangle shape and the handshake problem.
Triangular numbers
Pair numbers from both ends: 1 + 100 = 101, 50 times. Two consecutive triangular numbers make a square. n + 1 people shaking hands once each make Tₙ handshakes.
How to Use
- Enter n.
- Nothing else is needed.
- Press “Calculate” to see the triangular number and the next one.
Formula Used
Tₙ = n(n + 1) ÷ 2
Practical Examples
- Example 1
- T₁₀ = 55.
- Example 2
- 1 to 100: 5050.
Important Tips
- Sum a to b as T_b − T_(a−1).
- Consecutive ones make squares.
- Use it for handshakes.
Common Mistakes to Avoid
- Forgetting to halve.
- Using n + 1 terms.
- Counting each handshake twice.
Frequently Asked Questions
- 1 to 50?
- 1275.
- Is 36 triangular?
- Yes, the 8th.
- Handshakes among 10?
- 45.