Question

d)1-2+3 -4+5-6+ ... +2021-2022 = ​

Answer 1

$1 - 2 + 3 - 4 + 5 - 6 + ... + 2021 - 2022 =$

$(1 + 3 + 5 + ...2021) - 2( 1 + 2 +3 + ... + 1011) =$

$(0 \times 2 + 1) + (1 \times 2 + 1) + ... +( 2 \times 1010 + 1) - 2 \times \frac{1011 \times 1012}{2} =$

$2 \times (0 + 1 + ... + 1010) + 1 + 1 + ... + 1 - 1011 \times 1012 =$

$2 \times \frac{1010 \times 1011}{2} + 1 \times 1011 - 1011 \times 1012 =$

$1010 \times 1011 + 1011 - 1011 \times 1012 =$

$1011 \times (1010 + 1 - 1012) =$

$1011 \times ( - 1) = - 1011$

Answer 2

Răspuns:

$\red{ \underline{\bf - 1011 }}$

Explicație pas cu pas:

$\bf1-2+3 -4+5-6+ ... +2021-2022 =$

$\bf(1-2)+(3 -4)+(5-6)+ ... +(2021-2022) =$

$\bf\underset{de \: 1011 \: ori}{\underbrace{(-1)+( - 1)+( - 1)+ ... +(-1)}}=$

$\bf\underset{de \: 1011 \: ori}{\underbrace{-1 - 1 - 1 - ..... -1}} =$

$\red{ \underline{\bf - 1011 }}$

==pav38==