Alg10.2

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Find the fourth term in (\frac{3}{x}+y)^7\,

General term in the expansion is T_{r+1}=n\!C_r x^{n-r} y^r\,

To find the fourth term,here r=3\,

Hence T_4=7\!C_3 (\frac{3}{x})^{7-3} y^3\,

T_4=\frac{7!}{4! 3!} [\frac{3^4}{x^4} y^3]\,

T_4=\frac{7\cdot6\cdot5}{3\cdot2\cdot1} [\frac{81y^3}{x^4}]=\frac{2835y^3}{x^4}\,


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