/sci/ - Science & Math

>>15658917
>I wanted to solve f(x) = x^2 without doing its exponent.
>What does that even mean??
x^2 = 36
Wanted to find out that x was 6 without doing sqrt(36).

>you did (accidentally?) come up with the following

It was an accident because I had no idea what triangular numbers were, but it seems to resemble their formulas and then I found out about them.

>derivative argument
Don't do exponents.
Say x^2 is roughly equal to 2x.
In order to get to 36 you'd have to sum 2x over and over:
2(1) + 2(2) + 2(3) and so on.
2x is however only an approximation of the function (x+dx)^2
When dx is 1, its actual derivative is
2x * 1 + 1^2, or 2x + 1
So the difference between the approximation and actual function is just 1.
In reality you are doing
2(1) +1 + 2(2) + 1 + 2(3) + 1 and so on
But this is more convinient:
2 (triangular sum) + x

>I have no idea how you are expecting to calculating a series sum without knowing how long it is (x)
I don't know the first thing about series yet, can't even follow your math confidently but it's about time I guess.