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प्रश्न
Find the middle term in the expansion of `(x/"a" - "a"/x)^10`
उत्तर
Here, a = `x/"a"`, b = `-"a"/x`, n = 10
Now, n is even
∴ `("n"+2)/2=(10+2)/2` = 6
∴ Middle term is t6, for which r = 5.
We have, tr+1 = nCr an−r .br
t6 = `""^10"C"_5.(x/"a")^5.(-"a"/x)^5`
= 10C5 × −1
= `(-10!)/(5!5!)=-(10xx9xx8xx7xx6)/(5xx4xx3xx2xx1)`
= − 252
∴ Middle term is − 252.
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