User:Temperal/The Problem Solver's Resource3
Introduction | Other Tips and Tricks | Methods of Proof | You are currently viewing page 3. |
Summations and Products
Definitions
- Summations:
- Products:
Rules of Summation
, and in general
The above should all be self-evident and provable by the reader within seconds.
Derivation: We write as . Substituting n=1 gives while substituting n=2 gives . Hence, .
Now, , where we use the Hockey-Stick Identity. After some algebra, this comes out to .
This method can be generalized nicely; .
Particularly notable is the case ; we get . The reader can figure this out themselves.
Rules of Products
These should be self-evident, as above.