Binomial coefficient ((n+1) choose k) equals (n choose k) + (n choose (k-1))

Theorem

The following formula holds: $${{n+1} \choose k} = {n \choose k} + {n \choose {k-1}},$$ where ${n \choose k}$ denotes the binomial coefficient.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 3.1.4