Pascal's Rule/Mistake
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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 corrected in David Wells: Curious and Interesting Numbers (2nd ed.).
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $35$