binomial question - what am i doing wrong? (1 Viewer)

[kangarulz]

hi there, i've done a few "finding terms" questions and the answers always have a negative answer when i'm getting positive answers. just wondering if someone can point out what i'm doing wrong. here's the last question i did:

Find the term independent of x

(x - 1/x)⁶

T_k+1 = ⁿC_ka^n-kb^k

= ⁶C_k x^6-k(1/x)^k

=⁶C_k x^6-kx^-k

=⁶C_kx^6-2k

6-2k=0
-2k = -6
k=3

⁶C₃ = 20

but the answer in the book is neg 20

 

[vafa]

what you have done is excluding -1 from your general term. for clarification see my solution.

solution:
View attachment 13878

 

[NickP101]

b is -1/x not 1/x.

 

[jjames-hall]

i say its easier to think through it with a bit of old fashion logic, obviously the term will be independent when x^3 is divided by x^3. ie 6C3(x)^3(-1/x)^3 = -6C3 =-20. Saves me a lot of working and can work for ones a bit more complex too if you just think about it

 

[B35tY]

Yes i agree. To hell with the formula.

The formula can die for division of an interval too, i always do that in my head.

 

[renton]

can somebody please tell me the simplified version of

(nC(r+1))/nCr

for max term in binomial expansion

cheers

 

[Riviet]

can somebody please tell me the simplified version of

(nC(r+1))/nCr

for max term in binomial expansion

cheers

I'm pretty sure that simplifies to n-r

 

[vafa]

n-r+1/r*b/a