Question

Se consideră expresia E(x)=(2x-1) la a doua -3(x-3)(x+2)-(x-2)(x+1)
Demonstrați că E(1)+E(1 supra 2)+E(1 supra 3)+......E(1 supra 2020)=42420





Răspundeți repede vă rog!​

Answer 1

Sper ca te-am ajutat.

Answer 2

$E(x) = (2x-1)^2-3(x-3)(x+2)-(x-2)(x+1)$

$=4x^2-4x+1-3x^2+3x+18-x^2+x+2$

$=21$

$E(1)+E\left(\frac{1}{2}\right)+E\left(\frac{1}{3}\right)+...+E\left(\frac{1}{2020}\right)=$

$=21+21+21+\underset{\text{de 2020 ori}}{\underbrace{...}}+21\\ = 21\cdot 2020$

$=\boxed{42420}$