Bionomial theorem (1 Viewer)

[physician]

Find the greatest coefficient in the expansion of (5-2x)¹²

what do u guys get...

 

[Slidey]

There'll be 13 terms. You could just generate the coefficient of, say, the middle 4 and see which is greatest.

5^12 is pretty damn big.

It'd be something like:
5^12, 5^11 *-2*a, 5^10 *4*b, 5^9 *-8*c
So for it not to be the first term, a >2.5, for it not to be the 2nd term, b>25/4, c>125/8 et cetera.

At a guess, it might be the 8th term (since take a look at (1+x)^3 it is 1, 3, 3, 1 - obviously in the beginning the multipliers will cancel out the decreasing powers of 5, but the multipliers also increase as powers of 5 decrease, so... yeah I'd say somewhere in the middle 4)? I haven't covered binomial thoerem yet, though, so...

 

[Slidey]

(x+2)^4
=x^4+16x^3+24x^2+24x+16
(2x+3)^4
=16x^4+96x^3+648x^2+216x+81

My initial suspicion is correct: maximal coefficient is in the middle. The 8th coefficient.

 

[Estel]

The method I'd use:
General term:
Tk = 12Ck.5^(12-k)2^k(-1)^k
for greatest coefficient, k must be even (so Tk>0)
Then solve Tk+2/Tk >1 where k=0,2,4,6,8,10

 

[rama_v]

Couldnt you just use the formula method?
(n-r+1)/r .b/a >1 to determine r? Thats how I do these questions.

 

[Estel]

No because every second term is negative, and the question asks for the greatest coefficient, not coefficient of greatest magnitude.

 

[Slidey]

Not that it matters for this question.

 

[rama_v]

No because every second term is negative, and the question asks for the greatest coefficient, not coefficient of greatest magnitude.

ahh yes thats right. Thanks for clearing it up.

 

[Estel]

Arvin: have you heard the song "The Elements"?

 

[JamiL]

id use the n-r+1/r.b/a>1, and make sure n was an odd value. if that dose work the id expand it and us observation

 

[Arvin Sloane]

My god. Something happened here.

Everyone! Check your organs!

 

[physician]

cool thanks guys... that was a question from my half yearly.... i was kind of lost in the exam because it was too long and i started freaking out... binomial theorem being my second strongest topic after circle geomtry, isn't all too difficult.. i guess i should revise it a little more...

but thanks for everyones help....

 

[physician]

Do you still have all your organs Physician? Check!

come again

 

[physician]

Your organs man, your organs!

nope still intact

 

[Arvin Sloane]

I suppose you've got a heart in there?

 

[physician]

I suppose you've got a heart in there?

someones extremely Bored of Studies

 

[Arvin Sloane]

Intestines? Large or small? Spleen?

 

[acmilan]

Threads closed, way off topic