Question

Daca A=2017+2×(1+2+3+...+2016), atunci calculati A:2017
<Dau coroana!!!!>

Answer 1

Răspuns:

A : 2017 = 2017

Explicație pas cu pas:

A = 2017 + 2·(1+2+3+......+2016)

A : 2017 = ?

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Mai intai calculam suma S = 1+2+3+......+2016 ,

cu ajutorul Sumei lui Gauss:

1+2+....+n = (1+n)·n:2

S = 1+2+3+.....+2016 = (1+2016)·2016:2 = 2017·1008

Calculam pe A :

A = 2017 + 2·(2017·1008)

Dam factor comun pe 2017  =>

A = 2017·(1+2·1008) = 2017·(1+2016) = 2017·2017 = 2017²

=> A : 2017 = 2017²:2017 = 2017

A : 2017 = 2017