PIMSO 2022 - Mathematics - Grade 8 / Secondary 2 - National Round Question 2

What is the sum of this series up to its 100th term? $$1+\frac12+\frac13+\frac16+\frac16+\frac1{12}+\frac1{10}+\frac1{20}+\frac1{15}+\cdots$$