Can you explain the sum of 1 to 100?

The idea here is to pair your numbers up to get to the solution. If you were to put this through a calculator it would take you a while. However, if we simplify the problem to the sum of 1 to 10 you'll be able to check your answer on the calculator.Get your calculator out and do 1+2+3+4+5+6+7+8+9+10. What did you get? (Sum=55) Now, how can we do this without a calculator? Like I said before, the idea is to pair them up. If I tell you that you could pair 1 and 10, what's 1+10? What could the next pair be? 2+9= ? What is the pattern? How many 11's did you get? So have you found the sum in a simple way?
Now try the same trick with 1+2+3+4+ ... + 97+98+99+100. 1+100= ?, 2+99=?, 3+98=? But how many would you get? Think about what would happen in the middle ..... +47+48+49+50+51+52+53+54+... which ones pair up? So how many do you have? And what's the answer? You should have got 5050.

JS
Answered by Jasivan S. Maths tutor

2911 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

If x^2 + 4x + 3xy + y^3 = 6, find the first derivative.


Perhaps an introduction to integration with a simple integral, e.g. the integral of x^2


The line AB has equation 5x + 3y + 3 = 0. The point with coordinates (2k + 3, 4 -3k) lies on the line AB. How do you find the value of k.


Simplify 5p + 2q – 3p – 3q


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences