/sci/ - Science & Math

Easy.
<div class="math">(1+x+x^2+x^3)^n=(1+x)^n(1+x^2)^n=\left(\sum_{i=0}^n {n\choose i} x^i\right)*\left(\sum_{j=0}^n {n\choose j} x^{2j}\right)=\sum_{i=0}^n \sum_{j=0}^n {n\choose i}{n\choose j} x^{i+2j}</div>
Rearranging the summation to go first by the sum k=i+2j, then by j, we get <div class="math">\sum_{k=0}^{3n} \sum_{j=0}^n {n\choose k-2j}{n\choose j} x^k</div>

>>4283679
<div class="math">\left(\sum_{i=0}^n {n\choose i} x^i\right)*\left(\sum_{j=0}^n {n\choose j} x^{2j}\right)=\sum_{i=0}^n \sum_{j=0}^n {n\choose i}{n\choose j} x^{i+2j}</div>

>>4283683
http://en.wikipedia.org/wiki/Summation#General_manipulations
Middle of the list

what in t he fuck ?

so it's not solved yet?

what level of education is required to attempt to solve these problems. im going into undergrad level physics and i wish to learn mathematics in parralell. do you think that this kind of thing is within scope of that? what would this be defined as? all i can see is a proof that a function is equivilent to a sum to some terms.

>>4284251
in vector space

>>4283616
>>4283679
>mod posts sticky no one cares about so he can maintain the illusion that /sci/ is a real math board
>someone posts the answer they googled 15 minutes later
>all of /sci/ needs to scroll past the pointless sticky for the next 23 hours and 45 minutes to get to the delicious religion and philosophy threads

Can we stop these stupid threads already?

>>4284706
You can hide the thread if you do not wish to scroll past it all the time.

>>4284706
Shut your whore mouth. These threads are awesome and I like them, and I'm not even a mod.

>>4284706
Also, if you thought that problem was so hard that someone would have to google it to figure it out, you're full retard. This is seriously one of the easiest fucking problems I've ever seen.

Come on, factoring it like that is the obvious first step, then the next step is just the binomial theorem, and then you're done in two obvious steps.

>>4283683
That's called the "distributive property of addition." You were supposed to learn it in something called "seventh grade" if you hadn't already.

>>4284722

When someone uses the word "obvious" that many times, they're either compensating for the fact that they can't write or the fact that it took them hours to figure out (after looking the problem up in advance on the website) and they're too embarrassed to admit it.

It's k, not everyone can be as smart as mathfag or ponymath.

>>4284740
It's OBVIOUSLY too hard for you to deal with my superiority.

>>4284740
I was just mad people can't into math, and compensating for being 7 hours late.

The level of these varies massively. Any first year maths undergrad could solve this one, probably an able high schooler

>>4284978
I could have done it in high school. Fuck, I knew the binomial theorem in middle school. That's all you really need.

>>4284740
>not everyone can be as smart as ponymath.or mathfag

ftfy ^^

>>4285001
Oh, ponymath.

>mfw i always come on /sci/ late for these threads and they are already solved

time to come on here at midnight and beat you faggots

>>4284740
>>4284706
>they think that undergrads aren't capable of analysis and elementary number theory
holy fuck, are you people really that retarded?

>>4285035
>he thinks this problem has anything to do with either analysis or number theory
holy fuck, are you people really that retarded?

>>4285037
>sequences aren't elementary number theory
>putnam isn't analysis-oriented
really?

Know some combinatorics and factoring and answer is practically given to you

>>4285043
>>sequences aren't elementary number theory
So by your standard anything with some integer variables in it is a number theory problem?

>>putnam isn't analysis-oriented
On the test this one came from there are 4 analysis problems (out of 12)

>>4285056
>So by your standard anything with some integer variables in it is a number theory problem?
no, just simple classification. this is entirely irrelevant to what i'm arguing, by the way. i'm just stating that anyone with a first-year course in mathematics is capable of understanding and solving the problems on the putnam. the people who claim that others look up the answer when they obviously do not are annoying as hell.

>>4285064
>this is entirely irrelevant to what i'm arguing, by the way

It's relevant to the point of whether or not you know wtf you're talking about.

>>4285068
well then, how would you classify problems on the putnam?

the official description is the following:
>It is also expected that the self-contained questions involving elementary concepts from group theory, set theory, graph theory, lattice theory, number theory, and cardinal arithmetic will not be entirely foreign to the contestant’s experience.

>>4285076
You weren't talking about the test in general, you were talking about this one problem, and the people who didn't think you(?) solved it without googling.

wat

>>4285083
i did not even solve this problem, it was already solved when i entered this thread.

if you re-read what i stated:
>>they think that undergrads aren't capable of analysis and elementary number theory

it's pretty obvious i was referring to the entire test.

Is y = 2x a linear operator on R2 or on R? How can I check? Just looking for some quick intuitions about linear operators, feel free to ignore.

>>4285184
Do you even know what that means? If you did, it should be obvious how to check.

Check whether
T(u+v) = Tu + Tv
T(av) = a(Tv)

>>4285184
lmgtfy.com/?q=Linear+Operator

emsoupo has

>>4285241

That is right, but let's get back to our problem.

>>4284733
I'm pretty sure that's, like, 5th grade.

frosted butts

So now /sci/ does mods homework?
wow...

>>4287180
Whatever, Algebra was in middle school, even though there was plenty of it before then.