A Mathematical Anecdote Analogous to Chemical Resonance

What this little conundrum suggests is that in infinitely switching between two states, the final result is halfway in between. This is the reasoning behind the structure of benzene and the ionic carboxylate group.

s = 1 - 1 + 1 - 1 + ...

(-1) * s = (-1) * (1 - 1 + 1 - 1 + ...)   | *-1

1 + (-1) * s = 1 + (-1) * (1 - 1 + 1 - 1 + ...) | +1

1 - s = 1 - 1 + 1 - 1 + ...

1 - s = s

1 = 2 * s

s = 1/2


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