Question 30
Find the following sum:
$$\begin{aligned}&\left(\frac12+\frac13+\frac14+\frac15+\cdots+\frac1{29}\right)+\left(\frac23+\frac24+\frac25+\cdots+\frac2{29}\right)\\&+\left(\frac34+\frac35+\cdots+\frac3{29}\right)+\cdots+\left(\frac{27}{28}+\frac{27}{29}\right)+\frac{28}{29}.\end{aligned}$$
$$\begin{aligned}&\left(\frac12+\frac13+\frac14+\frac15+\cdots+\frac1{29}\right)+\left(\frac23+\frac24+\frac25+\cdots+\frac2{29}\right)\\&+\left(\frac34+\frac35+\cdots+\frac3{29}\right)+\cdots+\left(\frac{27}{28}+\frac{27}{29}\right)+\frac{28}{29}.\end{aligned}$$