Pascal's Rule/Mistake/First Edition

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary
$35$


Mistake

From the rule for constructing the triangle it follows that
$\paren {\dfrac n m} + \paren {\dfrac n {m + 1} } = \paren {\dfrac {n + 1} {m + 1} }$


Correction

The notation is wrong.

It ought to be:

$\dbinom n m + \dbinom n {m + 1} = \dbinom {n + 1} {m + 1}$


This has been partially corrected in David Wells: Curious and Interesting Numbers (2nd ed.), but the $+$ and $=$ signs have been omitted.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $35$
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