Binomial Theorem proof tips anyone? (1 Viewer)

[talisman]

Normally when I do topic "summaries" (i don't really), I write a list of ways I see certain questions or things you pick up on that aren't necessarily taught but you know just work.

Right now, binomial proofs are doing my head in a little bit. I know I'll get it eventually (hoping) but tips would be appreciated people

 

[Skeptyks]

Sorry, which proofs?

 

[Annihilist]

Sorry, which proofs?

.

 

[talisman]

Sorry, which proofs?

really?

 

[SpiralFlex]

You mean when you differentiate or integrate, shift and let some variable equal a number?

 

[Carrotsticks]

I think OP is talking about Binomial Identities and their proofs.

If that is the case, then the best tip I can give you is "Use the terms of the question as a clue". If it has something like:



Then the 'clue' would be to equate coefficients containing the binomial term 3 etc etc.

 

[SunnyScience]

I too struggled with these a couple of weeks ago. Go find the the "Success One" book (library if you don't have it) and attempt to answer all the bionomial questions (most are proof ones) or just look at the solutions in the back and you'll get the hang of it!

Goodluck.

P.s. I still kind of suck at them but i certainly improved by doing this.

 

[Skeptyks]

really?

I wasn't joking, there are a lot of different styled questions for Binomial theorem.
EDIT: I just got it, your talking about equating coefficients or LHS = RHS style questions. In that case, CarrotSticks tips is good and also, for the LHS = RHS ones, usually its just a differentiate, let x = a...

 

[mirakon]

This may help if u can read it, sorry for the poor picture quality

 

[talisman]

I wasn't joking, there are a lot of different styled questions for Binomial theorem.
EDIT: I just got it, your talking about equating coefficients or LHS = RHS style questions. In that case, CarrotSticks tips is good and also, for the LHS = RHS ones, usually its just a differentiate, let x = a...

sorry for that jibe. i think i am doing teh "LHS = RHS" methods but not literally stating LHS, RHS

 

[talisman]

I think OP is talking about Binomial Identities and their proofs.

If that is the case, then the best tip I can give you is "Use the terms of the question as a clue". If it has something like:



Then the 'clue' would be to equate coefficients containing the binomial term 3 etc etc.

yea with doing all the past hsc questions now, you definitely start to see the clues, some are more ambiguous than others

 

[jet]

is usually a hint to integrate, just like is usually a hint to differentiate.