Finding the greatest coefficient... (1 Viewer)

[Petyo]

hey if you're asked to find the greatest coefficient in some binomial expansion and the result turns out to be negative, what would you do?

 

[cassieagill]

omg get a spaceship the world is going to implode!!!!!!!!!!!!!!!!!!!!!

 

[scardizzle]

Post the actual question so we can explain it but i assume the expansion is something along the lines of (a-b)^n the greatest coeff is when T(r+1)/T(r) > 1

i'm not sure what to do from there

 

[annabackwards]

Post the actual question so we can explain it but i assume the expansion is something along the lines of (a-b)^n the greatest coeff is when T(r+1)/T(r) > 1

i'm not sure what to do from there

You simplify and solve for r.

@OP - if you got a negative answer, you've most likely done something wrong.

 

[Petyo]

hm here is the question:
(2x^2 - (3/x) )^11

 

[Petyo]

the result is said to be -11 547 360 but the question itself does not specify "magnitude" so I'm just kind of confused @@-

 

[annabackwards]

the result is said to be -11 547 360 but the question itself does not specify "magnitude" so I'm just kind of confused @@-

You basically find r and then sub it back into the formula (a)^(n-r) x b^r

I'll write up solutions for scan them by tomorrow if no one else has posted up solutions by then - just a bit busy relaxing right now after trials have finished today for me XD

 

[scardizzle]

i think greatest coefficient implies a positive magnitude

so usually the maximum coefficient would usually be when r = 7 but that gives us a negative term
i think the greatest term is when r = 8
our teacher told us how to do these q's but i forgot -_-

 

[Michaelmoo]

Yep, greatest coefficient in every exam/book I've read implies greatest magnitude.

EDIT: Although, usually in the final answer you'd omit the negative sign. Atleast thats how it is for us. You'd have to check specifically with your teacher though.

 

[annabackwards]

Greatest term does refer to the magnitude, as the others have said

Here's my working out - do excuse my horrible handwriting XD

Click here for solution

By the way, i knew it was negative because when r = 7 gives the 7+1 = 8th and every even term will be negative (notice the pattern when expanding: + - + - etc etc).

We don't omit the negative....

 

[Michaelmoo]

Greatest term does refer to the magnitude, as the others have said

Here's my working out - do excuse my horrible handwriting XD

Click here for solution

By the way, i knew it was negative because when r = 7 gives the 7+1 = 8th and every even term will be negative (notice the pattern when expanding: + - + - etc etc).

We don't omit the negative....

Yer my bad. You don't omit the negative for the final answer.

 

[cutemouse]

our teacher told us how to do these q's but i forgot -_-

Yuuuu BAKER!!! NOVICE!!!!!!

 

[scardizzle]

Greatest term does refer to the magnitude, as the others have said

Here's my working out - do excuse my horrible handwriting XD

Click here for solution

By the way, i knew it was negative because when r = 7 gives the 7+1 = 8th and every even term will be negative (notice the pattern when expanding: + - + - etc etc).

We don't omit the negative....

hypothetically how would you solve it if the questions asked for the greatest positive coefficient without having to guess and check?

 

[annabackwards]

hypothetically how would you solve it if the questions asked for the greatest positive coefficient without having to guess and check?

I'm not quite sure if there's a proper way, but if you take a look at Pascal's triangle you'll realise that the greatest negative coefficient would the middle term and the greatest positive coefficients would be the term before or after the negative term... so i guess you could find the largest coefficient (Tr+1) and just find coefficient for Tr or Tr+2.

That's just how i would approach it though XD

 

[copyfrogs]

I realise this thread is from 2009 but I'm working through the same question and can't figure out why the -3/x becomes just 3/x. If anyone can explain it that would be amazing!

 

[henry931]

because the question is asking for the greatest coefficient - as in the magnitude of the coefficient. So the sign of the 3/x doesnt matter when finding k, but will matter when writing the coefficient (as said before)