# Thread: Finding the greatest coefficient...

1. ## Finding the greatest coefficient...

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?

2. ## Re: Finding the greatest coefficient...

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

3. ## Re: Finding the greatest coefficient...

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

4. ## Re: Finding the greatest coefficient...

Originally Posted by 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
You simplify and solve for r.

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

5. ## Re: Finding the greatest coefficient...

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

6. ## Re: Finding the greatest coefficient...

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

7. ## Re: Finding the greatest coefficient...

Originally Posted by 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 @@-
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

8. ## Re: Finding the greatest coefficient...

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 -_-

9. ## Re: Finding the greatest coefficient...

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.

10. ## Re: Finding the greatest coefficient...

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

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

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....

11. ## Re: Finding the greatest coefficient...

Originally Posted by annabackwards
Greatest term does refer to the magnitude, as the others have said

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

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.

12. ## Re: Finding the greatest coefficient...

Originally Posted by scardizzle
our teacher told us how to do these q's but i forgot -_-
Yuuuu BAKER!!! NOVICE!!!!!!

13. ## Re: Finding the greatest coefficient...

Originally Posted by annabackwards
Greatest term does refer to the magnitude, as the others have said

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

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?

14. ## Re: Finding the greatest coefficient...

Originally Posted by scardizzle
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

15. ## Re: Finding the greatest coefficient...

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!

16. ## Re: Finding the greatest coefficient...

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)

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