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SMO 2023 Open Round 1 Question 2

SMO · SMO 2023 Open Round 1

Question 2

If $x=\dfrac11+\dfrac1{1+2}+\dfrac1{1+2+3}+\dfrac1{1+2+3+4}+\cdots+\dfrac1{1+2+3+\cdots+100}$, find the value of $\lfloor1010x\rfloor$.