👤

a=2021+2x(1+2+3+...+2020) a este p.p

Răspuns :


[tex]2021 + 2(1 + 2 + 3 + ... + 2020)[/tex]
Folosim Suma lui Gauss

[tex]2021 + 2 \frac{2020 \times 2021}{2} = \\ = 2021 + 2020 \times 2021 \\ = 2021(1 + 2020) \\ = {2021}^{2} [/tex]
Deci a este patrat perfect
a=2021+2×(1+2+3+...+2020)
a=2021+2×2041210
a=2021+4082420
a=4084441
4084441=2021 la puterea a doua