finding the greatest coefficient... (1 Viewer)

[micuzzo]

hey every1... just a quick question... can somebody explain this 1 to me... (2x-1)^5 .... no need for the whole thing... just the end bit... ie start from here: 6-k/-2kx I cant seem to get an answer....btw txtbk says +/-80 as final answer. thanks!

 

[raniaaa]

for greatest coefficient:
Tk+1 ≥ Tk
Tk+1 / Tk ≥ 1

(6-k) / 2k ≥ 1
6-k ≥ 2k
6 ≥ 3k
k ≤ 2

5C2 (2x)³ (-1)²
80x³

dunno why it's +/-

 

[micuzzo]

^ok im a bit confused... what happend to the negative denominator? also when working the highest coeff do we always state that Tk+1>Tk ? oh also... why is it ≥ and not just > my teacher didnt expl this properly.

 

[untouchablecuz]

ok, i've learnt as a rule, when its (ax-b)^n, disregard the negative when finding the greatest co-efficient

 

[untouchablecuz]

for greatest coefficient:
Tk+1 ≥ Tk
Tk+1 / Tk ≥ 1

(6-k) / 2k ≥ 1
6-k ≥ 2k
6 ≥ 3k
k ≤ 2

5C2 (2x)³ (-1)²
80x³

dunno why it's +/-

hallap rania binomiallllllllllllllllllllllll

 

[micuzzo]

why is it ≥ and not just >

 

[raniaaa]

why is it ≥ and not just >

oo wait it is just > my bad =)

 

[micuzzo]

oo wait it is just > my bad =)

okay.. so how do i no wen its meant to be ≥ rather than >.... but i think ur rite in saying its ≥ coz if not then how can u substitute the 2 if its <2

 

[raniaaa]

okay.. so how do i no wen its meant to be ≥ rather than >.... but i think ur rite in saying its ≥ coz if not then how can u substitute the 2 if its <2

my textbook uses just >
cos what if k has decimals... it has to be a whole number

 

[hayner]

k≤2 so k can be 2,1,0...etcso sub in k=2, coefficient=80sub k=1, coefficient=-80(but it's a bit wierd...cuz isn't 80>-80?? and don't they want greatest coefficient?)I think the reason why ≥ and not just > is because of pascal's triangle and how the coefficients of the expansion can be symmetrical so if T(K+1)=T(k) then equality holds

 

[micuzzo]

my textbook uses just >
cos what if k has decimals... it has to be a whole number

umm ok i see... only one thing... did u just disregard the negative denominator as untouchablez said. Oh but like i sed b4, if ur answer is k<2, how can we substitute k=2

 

[raniaaa]

i dunno i'm confused.

 

[micuzzo]

i dunno i'm confused.

okk lol... lets hope it doesnt come up... good luck

 

[annabackwards]

I suggest using Tk+1/Tk >= 1 and just making k be the nearest integer.

Don't get confused, because there's no = sign when it's Tk+1/Tk < 1. I have no idea why, just got taught that way :/

**You usually only use Tk+1/Tk >= 1 when finding the greatest coefficient, but you can also use Tk+1/Tk < 1 or both XD

 

[micuzzo]

I suggest using Tk+1/Tk >= 1 and just making k be the nearest integer.

Don't get confused, because there's no = sign when it's Tk+1/Tk < 1. I have no idea why, just got taught that way :/

**You usually only use Tk+1/Tk >= 1 when finding the greatest coefficient, but you can also use Tk+1/Tk < 1 or both XD

so thers no diff between saying Tk+1>Tk or Tk+1<Tk? is it just me or r the forum pages on other ppls comps displaying very strangely without pics

 

[annabackwards]

so thers no diff between saying Tk+1>Tk or Tk+1<Tk? is it just me or r the forum pages on other ppls comps displaying very strangely without pics

Nope, same thing. You usually would only use Tk+1>= Tk though but make sure you the sign is ">=" and not ">"!

 

[bmn]

I'm really confused about the signs and negatives as well, mainly because we got taught positives, but not negatives... Can somebody say what the main differences is with a negative? (ie (5-2x)^6 - not a question)) Also, do we have to use the tk+1>tk method? I just looked at it on Mathsonline, and it also had a "trial and error" method to find the greatest coefficient... If we don't have to use it, can we be asked for it?

 

[annabackwards]

I'm really confused about the signs and negatives as well, mainly because we got taught positives, but not negatives... Can somebody say what the main differences is with a negative? (ie (5-2x)^6 - not a question)) Also, do we have to use the tk+1>tk method? I just looked at it on Mathsonline, and it also had a "trial and error" method to find the greatest coefficient... If we don't have to use it, can we be asked for it?

Just do it like usual and disregard the negative sign then.

 

[Thecorey0]

Another method is using the formula (n-r+1)/r *(b/a) >=1

 

[untouchablecuz]

thats what you get after simplifing T_(k+1)/T_(k)>1