Question

11 Calculeaza: 2 · ( 1 + 2 + 3 + ... + 2014): 2015​

Answer 1

Explicație pas cu pas:

sumă Gauss

$\boxed {1 + 2 + 3 + ... + n = \dfrac{n \cdot (n + 1)}{2}}$

$2 \cdot (1 + 2 + 3 + ... + 2014) : 2015 = \\ = 2 \cdot \dfrac{2014 \cdot (2014 + 1)}{2} : 2015 \: \: \: \: \: \: \: \: \: \: \\ = 2014 \cdot 2015 : 2015 = \bf 2014 \: \: \: \: \: \: \: \: \: \: \: \: \:$

sau:

$2 \cdot (1 + 2 + 3 + ... + 2014) : 2015 = \\= 2 \cdot [2014 \cdot (2014 + 1) : 2] : 2015 \: \: \: \: \\ = 2014 \cdot 2015 : 2015 = \bf 2014 \: \: \: \: \: \: \: \: \: \: \: \: \:$