Question

Aratati ca numarul 2017+2(1+2+3...+2016)este patratul unui numar natural

Answer 1

2017 + 2•(1+2+3+...+2016) =

= 2017 + 2•2016•(2016+1)/2 =

= 2017 + 2•2016•2017/2 =

= 2017 + 2016•2017 =

= 2017•(1+2016) =

= 2017•2017 =

= 2017²

Answer 2

Explicație pas cu pas:

2017 + 2 × (1+2+3+...+2016) =

2017 + 2 × [2016 × (2016+1)] : 2 =

(2 se reduce)

2017 + (2016 × 2017) =

(dăm factor comun pe 2017)

2017 × ( 1 + 2016) =

2017 × 2017 =

2017^2 p.p

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