Binomial Identities

Hello_World

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Jun 22, 2022
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I'm just confused about where to start proving. Can anyone. help pls
 

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Steven G

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Dec 30, 2014
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Start with small values for n and see if you see a pattern. See what you get for n=2, n=3, n=4 ...., until you see a pattern. Then prove that result for n.
 

JeffM

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Sep 14, 2012
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I cannot stress enough Steven’s point.

You MAY be able to see a general result without any knowledge of a single example, but most of us are not that perceptive. Working out a few simple examples will probably give a clue or two about what a general result may look like. Staring at the page with a look of serious concentration and without experimentation is a fool’s errand. Try things. Popper drew a great distinction between the logical nature of validation and the psychological nature of discovery.

I am going to give you a second hint.

Do you have any familiarity with the meaning, if there is any, of [imath]\dbinom{1}{2}[/imath]? What does that suggest is the easiest example of n to experiment with.
 
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