PIMSO 2022 - Mathematics - Grade 10 / Secondary 4 - National Round Question 2

What is the sum of the series below up to its 1000th term? $$\frac1{12}+\frac1{24}+\frac1{24}+\frac1{48}+\frac1{40}+\frac1{80}+\frac1{60}+\cdots$$

Pattern convention: continue the pairs with consecutive-factor denominators.