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find the middle term of (x/a+a/x)^10

Dear student,

W e h a v e, {(\frac{x}{a} + \frac{a}{x})}^{10} T h u s, t h e e x p a n i s i o n w i l l h a v e (10 + 1) t e r m = 11 t e r m s t h e r f o r e t h e m i d d l e t e r m i n t h e e x p a n s i o n i s t h e 6 t h t e r m = {}^{10}C_{5} {(\frac{a}{x})}^{10 - 5} {(\frac{x}{a})}^{5} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5!}{5! \times 5 \times 4 \times 3 \times 2 \times 1} {(\frac{a}{x})}^{10 - 5} {(\frac{x}{a})}^{5} = \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1} {(\frac{a}{x})}^{5} {(\frac{x}{a})}^{5} = 252

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