- #1
Lancelot1
- 28
- 0
Dear All,
I am trying to prove the following identity:
\[\binom{n}{k}=\binom{n-2}{k}+2\binom{n-2}{k-1}+\binom{n-2}{k-2}\]
My attempt was based on transforming the binomial coefficients into fractions with factorials, and then elimintating similar expressions. Somehow it didn't work out.
I believe that this proof shouldn't be too long. Can you assist ?Thank you in advance.
I am trying to prove the following identity:
\[\binom{n}{k}=\binom{n-2}{k}+2\binom{n-2}{k-1}+\binom{n-2}{k-2}\]
My attempt was based on transforming the binomial coefficients into fractions with factorials, and then elimintating similar expressions. Somehow it didn't work out.
I believe that this proof shouldn't be too long. Can you assist ?Thank you in advance.