Question

f(x)=-2x+1
b) Calculati suma S= f(0)+f(1)+f(2)+...+f(2021)​

Answer 1

Răspuns:

S = -2020×2022

Explicație pas cu pas:

$f(x)=-2x+1 \\ f(0)= - 2 \times 0 + 1 \\ f(1)=-2 \times 1+1 \\ f(2)=-2 \times 2+1 \\ f(3)=-2 \times 3+1 \\ ... \\ f(2021)=-2 \times 2021+1$

$S= f(0)+f(1)+f(2)+...+f(2021) = ( - 2 \times 0 + 1) + ( - 2 \times 1 + 1) + ( - 2 \times 2 + 1) + ( - 2 \times 3 + 1) - + ... + (- 2 \times 2021 + 1) = - 2(0 + 1 + 2 + 3 + ... + 2021) + 1 \times 2022 = - 2 \times \frac{2021 \times 2022}{2} + 2022 = 2022 - 2021 \times 2022 = 2022(1 - 2021)= -2020 \times 2022$