User:Temperal/The Problem Solver's Resource3
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Summations and 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.