Question

Arătați că numărul a = 2×(1+2+3+...+2018)+2019 este patrat perfect




va rog

Answer 1

2 × ( 1 + 2 + 3 + ...... + 2018 ) + 2019 =

= 2 × 2018 × ( 1 + 2018 ) : 2 + 2019

= 2018 × 2019 + 2019 =

= 2019 × ( 2018 + 1 ) =

= 2019 × 2019 =

= 2019² → patrat perfect

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1 + 2 + 3 + .... + 2018 =→ aplic formula sumei lui Gauss

=  2018 termeni × [ 1 ( primul termen) + 2018 ( ultimul termen al sumei ) ]  : 2