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SMO 2021 Junior Round 1 Question 5

SMO · SMO 2021 Junior Round 1

Question 5

Which of the following is closest to the value of $$\frac1{\sqrt2+1}+\frac1{\sqrt3+\sqrt2}+\frac1{\sqrt4+\sqrt3}+\cdots+\frac1{\sqrt{2021}+\sqrt{2020}}\ ?$$
  1. 10
  2. 20
  3. 30
  4. 40
  5. 50