Question

calculeaza 1/3 +2/3+...+2016/3

Answer 1

Avand numitor comun, la numarator vom avea suma Gauss :
1+2+3+...+2016=(2016x2017)/2=2033136
2033136/3 = 677712

Answer 2

   
[tex]\displaystyle\\ \frac{1}{3} + \frac{2}{3}+ \dots + \frac{2016}{3} = \\\\ = \frac{1}{3} (1 + 2 + \cdots + 2016) =\\\\ =\frac{1}{3} \times \frac{2016 \times 2017}{2} =\frac{2016 \times 2017}{3 \times 2} =\\\\ = \frac{2016 \times 2017}{6} = 336 \times 2017=\boxed{\bf 677712}[/tex]