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butterflydreamer
 one year ago
BINOMIAL THEOREM question:
http://prntscr.com/8ib6g8
Find the numerically greatest coefficient in the expansion of (2  x^2/4)^10.
butterflydreamer
 one year ago
BINOMIAL THEOREM question: http://prntscr.com/8ib6g8 Find the numerically greatest coefficient in the expansion of (2  x^2/4)^10.

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butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.0I'm confused on what to do with the negative sign?? I know we use the formula: \[\frac{ T _{k+1} }{ T_{k}} = \frac{ n  k + 1 }{ k } \times \frac{ b }{ a }\]

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.0Or do we ignore the negative? O_O

Empty
 one year ago
Best ResponseYou've already chosen the best response.0I don't know what this is, so I don't know what they mean. I think the binomial is \[(a+b)^n = \sum_{k=0}^n \binom{n}{k}a^kb^{nk}\] So I'm not so sure what they're wanting here, I am guessing coefficient on x after it's all expanded out right?

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.0This is what i did but i'm not sure if i'm solving this correctly :S http://prntscr.com/8ib6g8

dan815
 one year ago
Best ResponseYou've already chosen the best response.2if negatives dont matter then that is right i think

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I know this doesn't really help with the problem all that much, but I would factor the 1/4 out of each term, that is just getting in the way in my opinion,\[\large\rm \left(2\frac{x^2}{4}\right)^{10}=\frac{1}{4^{10}}\left(8x^2\right)^{10}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yah I would imagine that's what they meant by "numerically greatest", like ignore the sign :O that sounds right.

dan815
 one year ago
Best ResponseYou've already chosen the best response.2sheesh why cant they just say magnitude or abs value .

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.0hmm i'm lost xD I don't know whether it will be 1280 or 1280... I think maybe it'll be 1280??

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1why x=1? :o does that just make the rest of the calculations easier or something?

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.0i actually have no idea LOLL. I just got taught to set x = 1 if there was no given value of x? So unless the question gave a specific value of x, you'd just plug in x = 1 :/ If they asked for the term independent of x, then you set x = 0

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I don't know that weird T formula 0_o I'mma do it the long way and see if that checks out.\[\large\rm \frac{T_{k+1}}{T_k}=\frac{\color{orangered}{\left(\begin{matrix}10 \\ k+1\end{matrix}\right)}2^{10(k+1)}\left(\frac{x}{4}\right)^{k+1}}{\color{orangered}{\left(\begin{matrix}10 \\ k\end{matrix}\right)}2^{10k}\left(\frac{x}{4}\right)^{k}}\]Which I guess simplifies down a bit right? Ummm\[\large\rm \frac{T_{k+1}}{T_k}=\frac{\color{orangered}{\frac{10!}{(k+1)!(10(k+1))!}}\left(\frac{x}{4}\right)^1}{\color{orangered}{\frac{10!}{k!(10k)!}}2^1}\]And more simplifying _\[\large\rm \frac{T_{k+1}}{T_k}=\frac{k!(10k)!}{(k+1)!(10(k+1))!}\cdot\left(\frac{x}{8}\right)\]and further _\[\large\rm \frac{T_{k+1}}{T_k}=\frac{(10k)}{(k+1)}\cdot\left(\frac{x}{8}\right)\]Hmmmm yah I'm seeing how you got 11 :O Thinking...

dan815
 one year ago
Best ResponseYou've already chosen the best response.21280 i read some post where numerical greatest means the magnitude of the number

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Not seeing how you got 11* blah

dan815
 one year ago
Best ResponseYou've already chosen the best response.2pls show me appreciation with your medals

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.0is there even a difference between "greatest coefficient" and "numerically greatest coefficient" ? o.o But alrighties, i guess i'll stick with 1280...

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Oh your formula works actually,\[\large\rm \frac{T_{k+1}}{T_k}=\frac{(10\color{royalblue}{(k)})}{(\color{royalblue}{k}+1)}\cdot\left(\frac{x}{8}\right)\] \[\large\rm \frac{T_{k+1}}{T_k}=\frac{(10\color{royalblue}{(k1)})}{(\color{royalblue}{k1}+1)}\cdot\left(\frac{x}{8}\right)\] \[\large\rm \frac{T_{k+1}}{T_k}=\frac{10k+1}{k}\cdot\left(\frac{x}{8}\right)\]Ok I'll simmer down XD

dan815
 one year ago
Best ResponseYou've already chosen the best response.2yes greatest coefficient means the biggest number where positive numbers are greater than the negative numbers Numerically greatest means the number that is farthest away from 0 or the origin

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.0LMAO Zepdrix xD Your dedication is so strong. Binomials give me headaches. Dan, wait, so if it is the number farthest away from 0 or the origin, wouldn't it be 1280?

butterflydreamer
 one year ago
Best ResponseYou've already chosen the best response.0okaaayyy ^_^ Thank you ALL~ <3.
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