Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
xEnOnn
Group Title
From this: \[(1+t+t^2)^5=\sum \binom{5}{r_1}\binom{5r_1}{r_2}t^{r_2}t^{2r_1}\]
How do I carry on to find out the values of \[r_1\] and \[r_2\]?
 2 years ago
 2 years ago
xEnOnn Group Title
From this: \[(1+t+t^2)^5=\sum \binom{5}{r_1}\binom{5r_1}{r_2}t^{r_2}t^{2r_1}\] How do I carry on to find out the values of \[r_1\] and \[r_2\]?
 2 years ago
 2 years ago

This Question is Closed

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
is your summation suppose to have limits?
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
yea...but this is just binomial so i just lazy to put them in...
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
that has to be the ugliest summation question i have ever seen
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
just looks ugly i have worked with these in like a couple years, so i guess to me its just looks crazy since my field doesn't use frequently; meaning i have fallen out of practice. ha ha ]
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
i have done this quite some time ago like last yr..but i recently need these again but forgotten how to continue from here...i remember i need to find out the coeffiicient value and then put them into an equation to solve for the r... but i'm stuck at finding the coefficient value...
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
I would go to wikipedia and search binomial theorem and see if you can glean the answer from that. It might help with the expansion of the binomial coefficient
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
i'm actually on wikipedia now... but i just couldn't figure out... i'm still trying though...
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
Ha ha I'm on it too trying to remember this stuff. lols
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
lol...the idea was to expand that \[(1+t+t^2)^5\] that got me started using binomial...and I thought I could do it until I tried that I realise i couldn't...
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
oh i see what you're doing just trying to expand yeah its not a binomial, its a trinomial
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
I think I need the values of \[r_1\] and \[r_2\] to expand, wouldn't I?
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
not sure with a binomial, they would sum up to 5
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
hmm... could it be \[r_2=5r_1\] and \[2r_1=5\]? But this would cause \[r_1=5/2\] which can't happen in such a thing since the coefficients must be integers... hmm...
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
your first equation i believe is wrong, r_2=5r_1 is incorrect. If that were true one your binomial coefficients would be 1 and that seems like unlikely simplification, but i could be wrong thats just my input
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
yea you are right. that is wrong. i was trying different ways to figure out an answer to it. haha..
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
its ok i would be doing the same thing =)
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
can't quite get the summation to work out here's the expansion though \[= t^{10}+5t^{9}+15t^{8}+30t^{7}+44t^{6}+50t^{5}+44t^{4}+30t^{3}+15t^{2}+5t+1\]
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
Well i think i got something that might help you. Knowing that this is a trinomial it must follow the form \[(a+b+c)^n=\sum_{i,j,k}^{n}\left(\begin{matrix}n \\ i,j,k\end{matrix}\right)*a^I*b^j*c^k\] meaning: \[t^{r_2}+t^{2r_1}=t^5\] since: i+j+k=5 which implies that \[r_2+2r_1=5\] thats as far as I've gotten and I'm tired hope maybe this inspires someone else to finish =)
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
Would this be right if I say \[r_2+2r_1=5\] and that \[r_2=5r_1\] and then solve simultaneously, to get \[r_1=1,r_2=5/2\]? But I remember that can't be a fraction.
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
doesn't seem right r1+r2 = 5 2r1 +r2 = 5 > r1 = 2r1 > 1=2 Equations contradict each other
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
where did you get r1+r2=5 from... I'm pretty sure one of the necessary equations is 2r1+r2=5. k=2r1 always, j=r2, and i=0
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
The one I got was because I thought from \[(1+t+t^2)^5=\sum \binom{5}{r_1}\binom{5r_1}{r_2}t^{r_2}t^{2r_1}\] The degree of \[r_2\] was created out of \[5r_1\] and \[2r_1\] was created out of the 5 in the \[ \binom{5}{r_1}\]. But I'm not sure if this is right.
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
\[\sum_{k=0}^{5}\sum_{j=0}^{5k}\sum_{i=0}^{5jk}\frac{5!}{i!j!k!}t^{j}t^{2k}\]
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
i think this is it
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
yes i agree that is a correct way of writing it, but even knowing that i=0 you still have two unknowns and only one equation
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
what do you mean by unknowns?
 2 years ago

xEnOnn Group TitleBest ResponseYou've already chosen the best response.0
I think he mean the k and j are unknowns and are needed to find the \[r_1\] and \[r_2\].
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
yea thats what i meant
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
well you are looking at every possible combination of i,j,k where sum equals 5
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
however the correct way of writing that is in summation form
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
sorry im kinda lost on how r1 and r2 have anything to do with it
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
your solving for r1 and r2 i believe
 2 years ago

dichiaraj Group TitleBest ResponseYou've already chosen the best response.2
in word form i believe the question would read what values for r1 and r2 would make this equation true
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
oh got it thanks
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
you said the 5r1 is incorrect, what should it be?
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.