Posted by steve on Tuesday, May 24, 2011 at 10:43pm.
which term in the expansion of (1/(3x^2)x)^15 is the constant term?
A. 10th
B. 11th
C. 12th
D. 13th

math  MathMate, Wednesday, May 25, 2011 at 12:17am
The constant term is the term where the power of x in the product (1/(3x²))^r*x^(15r) is zero, i.e.
(x^(2))^r*x^(15r)=x^0
=>
2r+(15r)=0
r=5
In general, a polynomial in x is written in descending order of the power of x.
So the powers of x for the expansion are:
x^0*(x^(2))^15 = x^(30)
...
x^10*(x^(2))^5 = x^0
...
x^12*(x^(2))^3 = x^6
x^13*(x^(2))^2 = x^9
x^14*(x^(2))^1 = x^12
x^15*(x^(2))^0 = x^15
Can you figure out which term gives the constant term?
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