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arata ca numarul a=81+2×81+3×81+....+49×81 este patrat perfect

Răspuns :

a=81+2×81+3×81+....+49×81=81×(1+2+3+4+..................+49)

(1+2+3+4+..................+49)- suma Gauss cu formula de calcul S=([n×(n+1)]:2

S=([49×(49+1)]:2=(49×50):2=1225=35²

a=81×35²=9²×35²=(315)² - patrat perfect