Răspuns:
[tex] \frac{2021}{2} [/tex]
Explicație pas cu pas:
[tex] \frac{1}{2022} + \frac{2}{2022} + \frac{3}{2022} + ... + \frac{2021}{2022} = [/tex]
[tex] = \frac{1 + 2 + 3 + ... + 2021}{2022} [/tex]
La numărător utilizăm formula
[tex]1 + 2 + 3 + ... + n = \frac{n(n + 1)}{2} [/tex]
[tex] = \frac{ \frac{2021 \times 2022}{2} }{2022} [/tex]
[tex] = \frac{2021 \times 2022}{2 \times 2022} [/tex]
[tex] = \frac{2021}{2} [/tex]
