Maths tricks · trick 8 of 25 · free

Add 1 to 100 in seconds — Maths trick for kids

Adding 1 + 2 + 3 + … + 100 one by one takes ages. A young genius can do it in seconds: pair the first and last numbers (1 + 100), the second and second-last (2 + 99) — every pair makes 101, and there are 50 pairs.

The trick

Pairs — “1 + 2 + … + n = n × (n + 1) ÷ 2”

  1. Pair the first and last numbers: each pair adds to n + 1.
  2. Count the pairs — or multiply n × (n + 1) and halve it.
  3. Odd numbers 1 + 3 + 5 + …: count them and multiply that count by itself.

Use it for: Adding long lists, counting handshakes or cricket balls in a series, and Olympiad puzzles.

Worked example: 1 + 2 + 3 + … + 100 = 5050

  1. Each pair adds to 1 + 100 = 101.
  2. 100 numbers make 50 pairs.
  3. 50 × 101 = 5050.

Check: 100 × 101 = 10100, and half of 10100 = 5050 ✓

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

Right: 0 · Tried: 0

🏁 Trick 8 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the ⭐ Young Genius Adder badge when you pass — and a certificate when you finish all 5 tricks of Part 2 · Number magic. You can still take the test without signing in.

🖨️ Sum of 1 to 100 Worksheet

✨ Free AI tutor

Ask the AI tutor about this trick

Why does it work? When should you use it? Ask in English, मराठी or हिंदी.

Sign in with Google to ask Free — 20 questions a day.

👩‍🏫 Maths tricks classes near you — online or at home

Prefer a real teacher? TalentJR teachers take live online classes anywhere in India and visit homes in selected cities. Tell us what you need and our team will call you with timings and fees.

Live online classesSmall groups or 1:1 with a teacher, from home, any city.
Teacher at homeA TalentJR teacher visits your home (selected cities).
At a centreClasses at a TalentJR partner centre near you, where available.
Badges, certificates & gifts A badge for every trick you pass, a certificate for every part you finish, plus TalentJR Points for daily practice. Mental maths Loved the tricks? Build real speed with Mental Maths Mastery.