Name: Shirley

If I were to add all the numbers between 1 and any number, I figured out I could use the formula (x squared plus x) divided by 2. With x being the last number. For example add together all the numbers between 1 and 1000. 1000 x 1000 =1,000,000. Plus 1000 = 1,001,000. Divided by 2 = 500,500. OR Add the numbers between 1 and 6 and you get 21. (6x6=36 plus 6 = 42 divided by 2 equals 21).

My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers?

I'm sure this is a very basic math puzzle, but I don't have a strong background in math. The question just came up at work today, so I thought I would try to find out.

Hi Shirley,

You're right about your formula and not only that if you look at your email you'll also see that you have the answer to your question. Suppose I asked you to add up all the numbers from 7 to 1000. Your answer for the sum from 1 to 1000 includes the sum from 1 to 6. If you subtract the two answers you have the sum of 7 + 8 + ... + 1000; it's

500,500 - 21 = 500,479 In general from (n+1) up to m you take (m*m + m) - (n*n+n) and divide by 2.


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