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Show that the middle term in the expansi...

Show that the middle term in the expansion of `((2x^2)/3+3/(2x)^(2))^(10) " is " 252.`

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`T_(r+1)=.^(10)C_(r) ((2x^(2))/3)^(10-r) xx (3/(x^(2)))^(r) = .^(10)C_(r) xx 2^(10-2r) xx 3 ^(2r - 10) xx x^((20-4r)).`
The expansion has 11 terms . So, middle term = 6th term.
`T_(6) = T_(5+1) = .^(10)C_(5) xx 2^(0) xx 3^(0) xx x^(0) = ((10 xx 9 xx 8 xx 7 xx 6 )/( 5 xx 4 xx 3 xx 2 xx 1 )) = 252.`
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