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PIMSO 2022 - Mathematics - Senior Secondary - National Round Question 1

PIMSO Maths · PIMSO 2022 - Mathematics - Senior Secondary - National Round

Question 1

What is the sum of this series up to its 100th term? $$\frac25+\frac15+\frac2{15}+\frac1{15}+\frac1{15}+\frac1{30}+\frac1{25}+\frac1{50}+\frac2{75}+\cdots$$

Pattern convention: continue the paired reciprocal-product pattern.