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SMO 2014 Open Round 1 Question 8

SMO · SMO 2014 Open Round 1

Question 8

In the sequence $$\frac14,\frac24,\frac34,\frac19,\frac29,\frac39,\ldots,\frac89,\frac1{16},\frac2{16},\ldots,\frac{15}{16},\frac1{25},\frac2{25},\ldots,\frac{24}{25},\ldots,$$ the $N$th term is $\frac{2014}{2025}$. Find $N$.