4 ms·
This is a fun example. The formula's easy to prove by induction, but discovering it is less obvious and this is an interesting way. It's the tip of the iceber
by domdip 13y ago
This is a fun example. The formula's easy to prove by induction, but discovering it is less obvious and this is an interesting way.
It's the tip of the iceberg though - generatingfunctionology is worth inspecting thoroughly.
- btilly 13y agoThere are actually perfectly routine ways to discover formulas like this one for this type of equation. See http://en.wikipedia.org/wiki/Recurrence_relation http://en.wikipedia.org/wiki/Recurrence_relation for some of the theory behind how to do it.