# Rational Number Expressible as Sum of Reciprocals of Distinct Squares/Mistake

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## Source Work

1992: David Wells: *Curious and Interesting Puzzles*:

- The Puzzles:
- Egyptian Fractions

## Mistake

*The sum of the series $1 + 1 / 2^2 + 1 / 3^2 + 1 / 4^2 \ldots = \pi^2 / 6$, so the sum of different Egyptian fractions whose denominators are squares cannot exceed $\pi^2 / 6$, but might equal, for example, $\frac 1 2$.*

## Correction

It is implicit that $1$ is not included in the set of Egyptian fractions.

We have that:

\(\ds \dfrac {\pi^2} 6\) | \(\approx\) | \(\ds 1.6449 \ldots\) | ||||||||||||

\(\ds \leadsto \ \ \) | \(\ds \dfrac {\pi^2} 6 - 1\) | \(\approx\) | \(\ds 0.6449 \ldots\) |

Hence the sentence should end:

*... cannot exceed $\pi^2 / 6 - 1$, but might equal, for example, $\frac 1 2$.*

## Sources

- 1992: David Wells:
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