Thread: How to form the correct equation

I suspect I am in the correct forum. However, due to partial or complete ignorance on my part, of disciplines above and including algebra, I may not be.
So in an effort save some time for this particular situation, I am presenting this here, before I embark on the learning curve,...if that is even possible.

Trying to define the equation I would use to find the value of a given number, using the following logic:

Given Number: 2 its value is: 1 determined via 1
Given Number: 3 its value is: 3 determined via 1+2
Given Number: 4 its value is: 6 determined via 1+2+3
Given Number: 5 its value is: 10 determined via 1+2+3+4
... to infinity

This feels obvious,...but I just can't seem to see it.

Try

Originally Posted by pickslides

Try

produces the correct result.

However, (and again please excuse my ignorance), it is unclear to me how you arrived at:

from:

Originally Posted by spfaff

[tex]However, (and again please excuse my ignorance), it is unclear to me how you arrived at:
from:

That is just one of the best known formulas in all mathematics.
It in easily proven using mathematical induction.

There is a story that when Gause was 8 years old, just to keep the students busy, his teacher assigned them the problem of adding all integer from 1 to 100. Gause immediately wrote 5050 on his slate, turned it over, and sat there. Presumably, he apparently recognized that if he reversed the sum he would have

That is, each pair adds to 100 and there are 100 such pairs: 101(100)= 10100 and since we have added twice each sum is 10100/2= 5050.

Similarly, you can continue to "n" rather than 100 to get

so there are n pairs, each summing to n+1: the total of the pairs is n(n+1) and the sum of each is