Solving $0=sum_{T=0}^{L}(2u^2A-2Ou)$ for $O$

Mathematics Asked on January 1, 2022

I know this seems like a very simple question, but I haven’t been able to find anything online regarding the answer to this.

Even WolframAlpha, which I usually use when I don’t know the answer to a problem like this, fails to find a result.

I need to rearrange for O (and then fully simplify): $$0=sum_{T=0}^{L}(2u^2A-2Ou)$$

Where $$u$$ is an expression that includes $$T$$, and $$A,O, L$$ are all variables

So far, my working includes:

$$0=sum_{T=0}^{L}(2u^2A)-sum_{T=0}^{L}(2Ou)$$

$$sum_{T=0}^{L}(2Ou)=sum_{T=0}^{L}(2u^2A)$$

$$2Osum_{T=0}^{L}(u)=2Asum_{T=0}^{L}(u^2)$$

$$O=frac{Asum_{T=0}^{L}(u^2)}{sum_{T=0}^{L}(u)}$$

If this is all correct, can this final expression of $$frac{Asum_{T=0}^{L}(u^2)}{sum_{T=0}^{L}(u)}$$ be simplified further?

Simplifying to $$Asum_{T=0}^{L}(u)$$ doesn’t seem to work

Related Questions

find the range of $x$ on which $f$ is decreasing, where $f(x)=int_0^{x^2-x}e^{t^2-1}dt$

2  Asked on December 4, 2020 by steven-lu

Differentiability for an integral function

1  Asked on December 4, 2020 by andereben

Solving a system of separable ODE’s

1  Asked on December 4, 2020 by costard

$Vert x_{n} – y_{n} Vert$is a cauchy sequence in $mathbb{F}$

1  Asked on December 4, 2020 by gaufler

equation of the form P (θ) = 0, where P is a polynomial, satisfied by the maximum likelihood estimator

0  Asked on December 4, 2020 by nisha

Evaluate $int_0^{infty } Bigl( 2qe^{-x}-frac{sinh (q x)}{sinh left(frac{x}{2}right)} Bigr) frac{dx}x$

2  Asked on December 3, 2020 by iridescent

How can one derive a partial differential equation from a function

1  Asked on December 3, 2020 by bob-pen

Dice Probability Dungeons and Dragons

3  Asked on December 3, 2020 by bangini

How can you derive an algorithm for dividing natural numbers?

0  Asked on December 3, 2020 by honza-prochazka

Expansion of the Frobenius norm

1  Asked on December 3, 2020 by wuannnn

On the definition of an algebra

1  Asked on December 3, 2020 by hakuna-matata

Distribution of a random variable given on the set of all natural number if …

0  Asked on December 3, 2020 by dabdya

Doubtful solution to an exercise on faithful flatness in Matsumura’s Commutative Algebra

1  Asked on December 3, 2020 by an-hoa

If $f(x)=frac{1-x}{1+x}$, then how do I explain graphically why $f(f(x))=x$?

4  Asked on December 3, 2020 by stupidgal123

*A: Prisoner A is selected for release. *B: The guard informs Prisoner A that Prisoner B is going to be released. Are A and B independent?

1  Asked on December 3, 2020 by t536373

Simplify the following sum $sum_{i=1}^nfrac1{n-(i-1)}$

1  Asked on December 3, 2020 by wild

What is a polynomial approximation?

3  Asked on December 2, 2020 by brilliant

Finding the smallest $k$ so that specific items are spaced exactly three apart

2  Asked on December 2, 2020 by troniix

Homotopic function question – very basic

2  Asked on December 2, 2020 by peter4075

Permutation involving different outcomes

1  Asked on December 2, 2020 by adam-mansfield