Binomial Identities

[Hello_World]

I'm just confused about where to start proving. Can anyone. help pls

 

[Steven G]

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.

 

[Subhotosh Khan]

I'm just confused about where to start proving. Can anyone. help pls

start with calculation of (1-x)ⁿ[1 - 1/x]ⁿ = [(1-x) * (1 - 1/x)]ⁿ

Using Binomial Expansion, please expand the above resulting function.

 

[JeffM]

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.

 

[AndreaSandell]

yes this question is very confusing.

 

[Subhotosh Khan]

yes this question is very confusing.

So what have you tried following these suggestions?