numerically greatest term in binomial theorem (1 Viewer)

[jxballistic]

Hi guys,
when a question asks for the numerically greatest term, which working out do i do?
so for e.g find the numerically greatest term of (1-2x)^9 when x = 1/3
My teacher says use the fitzpatrick book method which is "consider (1+2x)^9 because were finding numnerically greatest term" and then do the Tr+1/Tr >(or equal to) 1. But this only gives the positivee "greateet value" which is 224/9

Another method i learnt from my tutor is to do abs values i.e |Tr+1|/|Tr| >(or equal to) 1 which will gives 224/9 and -224/9.

Which method is hsc approved? And should the conclusion to the question be" the numerically greatest term is 224/9" or "the numerically greatest terms are 224/9 and -224/9"

 

[funnytomato]

both of these methods are essentially doing a similar thing
but the second one is better (intuitively makes more sense and also gives you the correct answer, IF you're careful)

it's up to how you interpret 'numerically greatest', I think it's just the one with largest absolute value for these kind of questions

 

[funnytomato]

so if you just follow the second method and solve |Tr+1|>|Tr|
you should be able to get r<3
which means that |T0|< |T1|< |T2|< |T3| > |T4|> |T5|> |T6|> ...
(the strict inequality in |T3| > |T4| is verified by substituting into Tr, but you could just say |T3| >= |T4|)
hence |T3| is the largest (or one of the largest if T4 happens to be equal to T3, which is not the case here)

and then you shouldn't get two values for T3 (= 9C3 (-2/3)^3)
hence it's the negative one

 

[funnytomato]

then the 1st method somewhat is doing a similar thing
once you know what's the largest number of the expansion of the sum
then the one for the difference is just the previous expansion alternating in sign, hence their absolute values are the same

 

[jxballistic]

Are they both hsc board of studies approved? So do I conclude with " numerically greatest term is 224/9"or "numerically greatesr terms are 224/9 and -224/9".
And Which method did you use ?

 

[braintic]

Are they both hsc board of studies approved? So do I conclude with " numerically greatest term is 224/9"or "numerically greatesr terms are 224/9 and -224/9".
And Which method did you use ?

There is no such thing as a board approved method.

 

[jxballistic]

There is no such thing as a board approved method.

So..... I can use either method?