根据下列短文，选择最佳选项。

    Sam likes soccer. He always watches soccer games on TV. His wife (妻子) Nina likes watching TV plays (电视剧). One evening at 7:00, Sam watches an interesting soccer game on TV. The TV also has a good TV play. It is Nina's favorite. She wants to watch it very much, but Sam sits before (在……之前) the TV. He doesn't let Nina watch the TV play. Nina is not happy, so she goes to her mother's home at 7:30 in the evening. When she comes into her mother's home, her father watches that soccer game, too.     

     “Where is my mother, Dad?”asks Nina.

     “She goes to your grandma's home,”says her father.

     “Why?”

     “I want to watch the soccer game, but she likes to watch a TV play.”

$\frac{1}{3}$  + $\frac{2}{3}$  =1

$\frac{7}{3}$  + $\frac{8}{3}$  + $\frac{10}{3}$  + $\frac{11}{3}$  =12

$\frac{16}{3}+\frac{17}{3}+\frac{19}{3}+\frac{20}{3}+\frac{22}{3}+\frac{23}{3}$ =39

…

则当m＜n且m，n∈N时， $\frac{3m+1}{3}+\frac{3m+2}{3}+\frac{3m+4}{3}+\frac{3m+5}{3}+\cdots +\frac{3n-2}{3}+\frac{3n-1}{3}$ =____（最后结果用m，n表示）