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anonymous
 4 years ago
the coefficient of x^2 in the expansion of (1 + x/5)^n, where n is a positive integer, is 3/5. Find the value of n.
How to do this???? :P
anonymous
 4 years ago
the coefficient of x^2 in the expansion of (1 + x/5)^n, where n is a positive integer, is 3/5. Find the value of n. How to do this???? :P

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[(1+x)^n=1+nx+\dbinom{n}{2}x^2+...\] in your case you will have \[1+n\frac{x}{5}+\dbinom{n}{2}\frac{x^2}{25}+ ...\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so basically i need to multiply 1/25 and \[\left(\begin{matrix}n \\ 2\end{matrix}\right)\], but how do I do that?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and equate it to 3/5.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so you know that \[\frac{n(n1)}{2}\times \frac{1}{25}=\frac{3}{5}\] \[\frac{n(n1)}{2\times 25}=\frac{3}{5}\] \[\frac{n(n1)}{10}=3\] \[n(n1)=30\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and since n is a whole number, only possible answer is \[n=6\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0wait, sorry, I don't get why n(n  1)/2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0to compute \[\dbinom{n}{k}\] you do not really use \[\frac{n!}{k!(nk)!}\] because it it is too much work, you just cancel. but we can write it out anyway

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\dbinom{n}{2}=\frac{n!}{2!(n2)!}\] ok?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ohhh. so if it was the coefficient of x^3, then we would do n(n  1)(n  3)/3 ??

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0then numerator is \[n\times (n1)\times (n2)!\] so you can cancel the \[(n2)!\] and get \[\frac{n(n1)}{2}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0it would be \[\frac{n(n1)(n2)}{3!}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0don't forget the factorial in the denominator

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0^sorry, that's what I meant to type :P Got it.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So, what's up, satellite??? haven't been here in a while :P

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0not much. where you been?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Sitting at home, studying for my mocks _. Ohhh, and i've got braces. i look WEIRD.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0been a month it seems

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well, i know. ^nopee, not much, but after a few hours they're tickling me :P And I feel like a kid, 'cause over here most people had their braces off by the 7th / 9th grade, and i'm starting in the 10th.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0But i've got a pretty blue, AND it's only for a year, so it's cool.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well at least they are a color and not those awful railroad tracks!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0*7th/8th grade. I KNOW, those are horrid. My brother didn't put any colours  I killed him for it. Idiot.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0More than that, I know some people who have gotton the clear, translucent braces, not the metal ones, and they've put colours on them. Kinda kills the whole point of seethrough ones, doesn't it???

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the new thing seems to be to make you have them twice. once around 6th /7th, then a year off, then back again. i think it is just a way to get more money out of parents

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0See??/ i'm such a nice girl, I became your fan :P
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