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 Hockeystick Identity. After some algebra, this comes out to
.
This method can be generalized nicely; .
Rules of Products
These should be self-evident, as above.