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SMO 2018 Junior Round 1 Question 2

SMO · SMO 2018 Junior Round 1

Question 2

Find the value of $$\begin{aligned}&\left(\frac 12+\frac 13+\frac 14+\cdots+\frac 1{2018}\right)\left(1+\frac 12+\frac 13+\frac 14+\cdots+\frac 1{2017}\right)\\&-\left(1+\frac 12+\frac 13+\frac 14+\cdots+\frac 1{2018}\right)\left(\frac 12+\frac 13+\frac 14+\cdots+\frac 1{2017}\right).\end{aligned}$$
  1. $\frac 1{2017}$
  2. $\frac 1{2018}$
  3. $\frac{2017}{2018}$
  4. $1$
  5. $\frac{2019}{2018}$