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M=2021+2•(1+2+3+...+2020)
Ar arătați că este patrat perfect.​


Răspuns :

Răspuns:

M=2021+2•(1+2+3+...+2020)

paranteza o calculam cu suma lui Gauss

M=2021+2·(2020·2021)/2

M=2021+4082420

M=4084441=2021×2021=2021²→ pp

√4084441=2021

M = 2021+ 2((2020•2021)/2) - (suma Gauss)
M = 2021 + 2(1010•2021
M= 2021 + 2020 • 2021
M = 2021(1 + 2020) - (factor comun 2021)
M = 2021•2021 = 2021^2 ——> patrat perfect