Find the 4th term from the beginning and `4^(th)` term from the end in the expansion of `(x+2/x)^9`

Explanation

Let `T_{{r}+1}` be the 4th term from the end.

Then, `T_{r+1}` is `(10-4+1)` th, i.e., 7 th, term from the beginning.

`therefore T_{7}=T_{6+1} `

`=\ ^{9} C_{6}(x^{9-6})(frac{2}{x})^{6} `

`=frac{9 times 8 times 7}{3 times 2}(x^{3})(frac{64}{x^{6}}) `

`=frac{5376}{x^{3}}`

4th term from the beginning `=T_{4}=T_{3+1}`

`therefore T_{4}=\ ^{9} C_{3}(x^{9-3})(frac{2}{x})^{3} `

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