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

## Source Work

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, $\frac 1 2$.