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Find the coefficient of x^(25) in expans...

Find the coefficient of `x^(25)` in expansion of expression `sum_(r=0)^(50)^(50)C_r(2x-3)^r(2-x)^(50-r)` .

Text Solution

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`underset(r=0)overset(50)sum.^(50)C_(r) (2x-3) .^(r)(2-x)^(50-r)`
`= ((2-x)+(2x-3))^(50)`
`= (x-1)^(50)`
`= (1-x)^(50)`
`=.^(50)C_(0) - .^(50)C_(1)x"……"-.^(50)C_(25)x^(25)+"……'`
Therefore, Coefficient of `x^(25)` is `-.^(50)C_(25)`.
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