Binomial theorem greatest term/coefficent 'formula'? (1 Viewer)

[elbatiolpxeho]

In Cambridge's worked example they expand the binomial into those factorial thingys which takes a while to simplify, after doing plenty of these questions I've noticed that,



Can I just pull this out? Is it a recognised formula or something? I haven't seen a single mention of it in Cambridge :S

 

[GENIUS1234]

you can do that if you want to fail, bloody idiot .

 

[Drongoski]

Can I just pull this out? Is it a recognised formula or something? I haven't seen a single mention of it in Cambridge :S

Even when correct, it is not a generally-accepted formula. So it's rather risky. Don't do what Galois did.

 

[elbatiolpxeho]

who is galois?

 

[SpiralFlex]

French Mathematician.

 

[bleakarcher]

Isn't T(k+1)=nCk*p^k*q^(n-k)?

 

[RealiseNothing]

Isn't T(k+1)=nCk*p^k*q^(n-k)?

That's T(k) I think.

 

[bleakarcher]

I think they defined them differently to the way I do.

 

[bleakarcher]

Since, when you think about it, the first term T(1) would contain nC0.

 

[D94]

Isn't T(k+1)=nCk*p^k*q^(n-k)?

This is correct.

 

[bleakarcher]

Can someone help me out? I have recently started learning binomial theorem and I came across this video:

http://www.slideshare.net/nsimmons/12x1-t08-04-greatest-coefficients-terms

and at about 5 minutes and 30 seconds when he is solving an inequality he multiplies both sides by k not k^2. Watch the video and you will understand what am I saying really. Anyone care to help?

 

[D94]

Can someone help me out? I have recently started learning binomial theorem and I came across this video:

http://www.slideshare.net/nsimmons/12x1-t08-04-greatest-coefficients-terms

and at about 5 minutes and 30 seconds when he is solving an inequality he multiplies both sides by k not k^2. Watch the video and you will understand what am I saying really. Anyone care to help?

Because k is always positive (it's a term) so it doesn't matter if you multiply by k or k^2. It doesn't change the inequalities sign.

 

[RealiseNothing]

Can someone help me out? I have recently started learning binomial theorem and I came across this video:

http://www.slideshare.net/nsimmons/12x1-t08-04-greatest-coefficients-terms

and at about 5 minutes and 30 seconds when he is solving an inequality he multiplies both sides by k not k^2. Watch the video and you will understand what am I saying really. Anyone care to help?

k can't be negative, so it's not necessary to square it? That's the only reason I can think of, because when you rearrange it you get:

(63-3k)/2k > 1

(63/2k)-(3/2) > 1

63/2k > 5/2

63/k > 5

So k must be positive.

 

[bleakarcher]

Ah ok lol, I understand now thanks D94.

 

[ohexploitable]

Isn't T(k+1)=nCk*p^k*q^(n-k)?

no, you can define it however you want

i've found that is much more intuitive

it just means i start counting at 0, i.e. T(0) is the first term

but it really doesn't fucking matter okay