Posted by **anoynomous** on Friday, March 22, 2013 at 1:17pm.

coefficient of x^39 in the expansion of [(1/x^2) + x^4)]^18

- maths-binomial theorem -
**Reiny**, Friday, March 22, 2013 at 2:15pm
Use the general term

term(n+1) = C(18,n) (1/x^2)^(18-n) (x^4)^n

= C(18,n) (x^(-36 +2n) ) (x^4n)

= c(18,n) x^(2n - 36)

ahhh, trick question,

to have a term with x^39 , 2n-36 = 39

there is no whole number solution,

**so there is no term with x^39**

e.g. --- take the first few terms

[(1/x^2) + x^4)]^18

= (1/x^2)^18 + 18(1/x^2)^17 (x^4) + 153 (1/x^2)^16 (x^4)^2 + ..

= x^-36 + 18x^-30 + 153x^-24 + ..

the exponent go

-36 -30 -24 .. missing the 39

## Answer this Question

## Related Questions

- maths-binomial theorem - how can we show that there is no constant in the ...
- Integrated Math 1 - What is the coefficient of the xy^2 term in the expansion of...
- Math - another question - "In the expansion of (2-ax)^5 the coefficient of x^2 ...
- Maths - Determine the coefficient of x^5 in the binomial expansion of (2-3x)^7?
- maths-binomial theorem--plse help - find the greatest term in the expansion of (...
- Math - Use the Binomial Theorem to determine the coefficient of x^14 in the ...
- maths - Use binomial theorem to to expand squareroot of 4+x in ascending powers ...
- maths - binomial theorem - Write and proof binomial theorem for rational indices...
- same type of binomial theorem question - Question: Find the first 3 terms in the...
- maths - find the first 3 terms in the expansion of (x+4)(1+3x)^-2 as a series in...