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SMO 2020 Junior Round 1 Question 25

SMO · SMO 2020 Junior Round 1

Question 25

What is the value of
$$\begin{aligned}&\left(\frac12+\frac13+\frac14+\frac15+\cdots+\frac1{37}\right)+\left(\frac23+\frac24+\frac25+\cdots+\frac2{37}\right)\\&\quad+\left(\frac34+\frac35+\frac36+\cdots+\frac3{37}\right)+\cdots+\left(\frac{35}{36}+\frac{35}{37}\right)+\frac{36}{37}?\end{aligned}$$