Question 1205236
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The problem is posted incorrectly.<br>
The sequence of characters "1/2x^2" is ambiguous.<br>
If that means {{{(1/2)x^2}}}, then there is of course no constant term in the expansion.<br>
But if it means (as it surely was intended to!) {{{1/(2x^2)}}}, then there is a constant term.<br>
Any student who is working on a problem like this should have enough experience with mathematics to know that proper use of parentheses is important.<br>
Assuming the latter meaning, the constant term will occur when the {{{4x^3)}}} term is to the 6th power and the {{{1/(2x^2)}}} term is to the 9th power.  That constant term is<br>
{{{(C(15,6))(4^6)((-1/2)^9)=(5005)(2^12)(-2^(-9))=5005(-2^3)=5005(-8)=-40040}}}<br>
ANSWER: -40040<br>