Alg10.3

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Find the middle term of the expansion (\frac{x}{y}+\frac{y}{x})^8\,

The expansion contains 9 terms in it.

Therefore, the middle term is the 5th term.

T_5=T_{4+1}=8\!C_4\cdot (\frac{x}{y})^{8-4}\cdot (\frac{y}{x})^4\,

T_5=8\!C_4 \cdot (\frac{x^4}{y^4})(\frac{y^4}{x^4})=8\!C_4\,

8\!C_4=70


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