3 term binomial? (1 Viewer)

[cheesegrater]

can anyone help me ive got no idea nver seen a question like this before
find the term independent of x in
(1 + x + 1/x)^5
thanks

 

[jogloran]

I think you treat it as (1 + (x + 1/x))^5, then expand at for (1+x)^n.

 

[Grizzly]

wherd u get it from ?
Unlikely it would appear.


And, dont quote me in ~12hrs

 

[ND]

If it's got 3 terms, it's not a binomial.

Anyway yeh, i'd let u=1+1/x and just expand twice.

 

[freaking_out]

Originally posted by jogloran
I think you treat it as (1 + (x + 1/x))^5, then expand at for (1+x)^n.

actually bring every thing under common denominator and take out the denominator to get:

1/x^5(x(x+1) + 1)^5

yeah, then that should b easier from there.

questions like these are in the syllabus i've seen it in various texts, and hence they might come on the exam 2moro.

 

[ND]

Ok let me post up a more 'elegant' method, i didn't wanna post it before cos i didn't feel like explaining it to anyone who asked, but what the hell..

ok let a=1, b=x, c=1/x
now, every term of teh expansion obivoulsy has to be to index 6, and for a constant term, this can be done the following ways:

a^6, a^3bc, ab^2c^2.

Now to get the coefficient of teh constant tern, add the number of ways these can be attained.

i.e. 1 + 5!/2!*2! + 5!/3! = 51.

 

[Constip8edSkunk]

interesting way. i like it.

but the question remains... will the marker accept it without you writing several paragraphs explaining it

 

[bMaN oNe]

Originally posted by ND
Ok let me post up a more 'elegant' method, i didn't wanna post it before cos i didn't feel like explaining it to anyone who asked, but what the hell..

ok let a=1, b=x, c=1/x
now, every term of teh expansion obivoulsy has to be to index 6, and for a constant term, this can be done the following ways:

a^6, a^3bc, ab^2c^2.

Now to get the coefficient of teh constant tern, add the number of ways these can be attained.

i.e. 1 + 5!/2!*2! + 5!/3! = 51.

I have NO idea how u got that :S I'll just stick with the longer methods (Although this question is still really tuff)

 

[redslert]

ND that's dam complex!

2u/3u people would not understand! no wonder you said you didn't want to explain...or your hiding secrets

 

[freaking_out]

Originally posted by redslert
ND that's dam complex!

2u/3u people would not understand! no wonder you said you didn't want to explain...or your hiding secrets

yeah, he's like that, u know 1337.