f-x-y-f-x-f-y-x-y-f-4-10-finde-f-2022-

Question Number 190704 by mathlove last updated on 09/Apr/23

f (x + y) = f (x) + f (y) + x \cdot y

f (4) = 10 f i n d e f (2022) = ?

Answered by mahdipoor last updated on 09/Apr/23

f (n + 1) = [f (n)] + f (1) + n =

[f (n - 1) + f (1) + (n - 1)] + f (1) + n = \dots

= (n + 1) f (1) + \frac{n (n + 1)}{2}

\Rightarrow f (4) = 4 f (1) + \frac{3 \times 4}{2} = 10 \Rightarrow f (1) = 1

f (2022) = 2022 f (1) + \frac{2021 \times 2022}{2} = 1011 \times 2023