find the coefficient of x^5 in the expansion of( 2x^3-1/3x^2)^10
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Step-by-step explanation:
Let S=1+2x+3x2+4x3+…
=>xS=x+2x2+3x3+4x4+…
S−xS=(1)+(2–1)x+(3–2)x2+(4–3)x3+…
S(1−x)=1+x+x2+x3+…=11−x
=>S=(1−x)−2
(1+2x+3x2+…)−32=S−32
=[(1−x)−2]−32
=[1−x]3=1−3x+3x2−x3
There is no coefficient of x5 in this expression. Hence, the coefficient is 0.
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