IKMC 2027 - Grades 7-8 - Self-study SET 15 - Thematic Batch 3 Question 24

For which n does $\frac12+\frac1{2+4}+\frac1{2+4+6}+\cdots+\frac1{2+4+\cdots+2n}=\frac{2013}{2014}$ hold?