Answer:
Step-by-step explanation:
[tex]n=1:\ \dfrac{1}{3} = \dfrac{1*2}{6}\\n=2:\ \dfrac{1}{3}+\dfrac{2}{3} = \dfrac{3}{3}=1=\dfrac{2*3}{6}=1\\n=3:\ \dfrac{1}{3}+\dfrac{2}{3}+\dfrac{3}{3} = \dfrac{6}{3}=2=\dfrac{3*4}{6}=2\\\\We\ suppose \ the\ property\ true\ for \ n :\\\\\dfrac{1}{3}+\dfrac{2}{3}+\dfrac{3}{3}+...+\dfrac{n}{3}=\dfrac{n*(n+1)}{3}\\\\\dfrac{1}{3}+\dfrac{2}{3}+\dfrac{3}{3}+...+\dfrac{n}{3}+\dfrac{n+1}{3}\\\\=\dfrac{n*(n+1)}{6}+\dfrac{n+1}{3}\\\\=(n+1)*(\dfrac{n}{6}+\dfrac{1}{3})\\\\=(n+1)*(\dfrac{n+2}{6})\\[/tex]
The property is true for n+1
