Question

x=(1+2+3+.....2000)÷2000×2

Answer 1

Calculam cu ajutorul Sumei lui Gauss: 

x=(1+2+3+...+2000):2000×2
x=2000×2001:2:2000×2

Se reduce "÷2" cu "×2"
Se reduce "÷2000" cu "2000×"

Rezultatul este : 2001

Answer 2

$\displaystyle x=(1+2+3+....+2000):2000\cdot2 \\ \\ \boxed{ \frac{n(n+1)}{2} } \\ \text{se aplica la sirul 1+2+3+...+n} \\\\ \\ \frac{2000(2000+1)}{2}= \frac{\not2000\cdot2001}{\not2}= 1000 \cdot 2001 \\ \\ \\ \frac{1000\cdot2001}{\not2000}\cdot\not2 = \frac{\not1000\cdot2001}{\not1000} = 2001$