omg get a spaceship the world is going to implode!!!!!!!!!!!!!!!!!!!!!
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?
omg get a spaceship the world is going to implode!!!!!!!!!!!!!!!!!!!!!
gilly gilly gilly, fishy fishy fishy
^^^^^^^^^^^^
....i really am a dill as my username was meant to be 'cassieadill' ... whoops
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
Last edited by annabackwards; 24 Aug 2009 at 10:35 PM.
HSC Courses: Extension 1 + 2 maths, Chemistry, Physics, Modern History and Advanced English
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hm here is the question:
(2x^2 - (3/x) )^11
the result is said to be -11 547 360 but the question itself does not specify "magnitude" so I'm just kind of confused @@-
HSC Courses: Extension 1 + 2 maths, Chemistry, Physics, Modern History and Advanced English
ATAR aim: 99.00.... reached
Uni Course: Civil Engineering @ UNSW. Timetable is here. Actually get a day off for once because of an awesome online general ed course
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 -_-
Last edited by scardizzle; 24 Aug 2009 at 10:42 PM.
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.
Last edited by Michaelmoo; 25 Aug 2009 at 8:57 AM.
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....
HSC Courses: Extension 1 + 2 maths, Chemistry, Physics, Modern History and Advanced English
ATAR aim: 99.00.... reached
Uni Course: Civil Engineering @ UNSW. Timetable is here. Actually get a day off for once because of an awesome online general ed course
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
HSC Courses: Extension 1 + 2 maths, Chemistry, Physics, Modern History and Advanced English
ATAR aim: 99.00.... reached
Uni Course: Civil Engineering @ UNSW. Timetable is here. Actually get a day off for once because of an awesome online general ed course
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!
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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