mathsbinomial theorem
posted by anoynomous .
coefficient of x^39 in the expansion of [(1/x^2) + x^4)]^18

Use the general term
term(n+1) = C(18,n) (1/x^2)^(18n) (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 , 2n36 = 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
Respond to this Question
Similar Questions

Math  another question
"In the expansion of (2ax)^5 the coefficient of x^2 is 5. Find the value of a". I know I have to use the binomial theorem to help me, but I don't know how. 
Math
Use the Binomial Theorem to determine the coefficient of x^14 in the expansion of (3x^2 − 1/ 3)^ 16 . Express the coefficient as a fraction in its lowest terms. Please help me with this I'm getting nowhere. And please explain … 
maths
Use binomial theorem to to expand squareroot of 4+x in ascending powers of x to four terms.Give the limits for which the expansion is valid 
Maths
Determine the coefficient of x^5 in the binomial expansion of (23x)^7? 
Integrated Math 1
What is the coefficient of the xy^2 term in the expansion of (3x + y)^3? 
maths  binomial theorem
Write and proof binomial theorem for rational indices? 
mathsbinomial theoremplse help
find the greatest term in the expansion of (1+x) raised to thepower of10, x=2/3 
mathsbinomial theorem
how can we show that there is no constant in the expansion of [2x – (x^2/4)]^9 
binomial expansion help!!!
in the expansion of (1+x)^(n+1) the coefficient of x^4 is 6k and in the expansion of (1+x)^(n1) the coefficient of x^2 is k.find the value of k and n, for n>2? 
precalculus
Can you check my answers? 1.Use the Binomial Theorem to expand and simplify the expression. (2  3x)3 27x3 + 104x2  36x + 8 27x3 + 54x2  36x + 8 27x3 + 8 27x3 + 54x2  18x + 8 answer:b 2.Find the 5th term in the expansion of