General Methods for Finding a Closed Form (Methods 0 - Look it Up and 1 - Guess & Prove)

Based on the book, Concrete Mathematics, by Graham, Knuth, and Patashnik.  (Chapter 2.5)  Given a summation - how do you find a closed form?  Method 0 - Look it up.  Method 1 - Guess and Prove by Induction.
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