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Erdős Problem #270 — Irrationality of sums of reciprocals of growing products

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Let f:N→Nf:\mathbb N→\mathbb N satisfy f(n)→∞f(n)→∞. Must the series ∑n≥1((n+1)(n+2)⋯(n+f(n)))−1∑_{n≥1}((n+1)(n+2)⋯(n+f(n)))^{-1} be irrational?

References

Primary source

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

Additional references

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

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