Alg10.5

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Find the constant term in the expansion of (3x-\frac{5}{x^2})^9\,

T_{r+1}=9\!C_r\cdot(3x)^{9=r}\cdot(\frac{-5}{x^2})^r=9\!C_r\cdot3^{9-r}\cdot(-1)^r\cdot(\frac{5^r}{x^2r}\,

9\!C_r 3^{9-r}\cdot 3^{9-r}\cdot 5^r\cdot(-1)^r\cdot x^{9-3r}\,

To get the constant term of the expansion we have to find r sothat 9-3r=0,r=3\,

Hence the 4th term is the one independent of x\, that is the constant term.

Therefore T_4=9\!C_3 \cdot3^{9-3}\cdot5^3\cdot(-1)^3=-9\!C_3.3^6\cdot5^3\,


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