Find the coefficient of `x^(-25)` in the expansion of `((x^(2))/(2)-(3)/(x^(3)))^(15)`

Answer

N/a

Explanation

`T_(r+1)=^(15)C_(r)((x^(2))/(2))^(15-r)(-(3)/(x^3))^(t)`
`=^(15)C_(r).(x^(30-2r))/(2^(15-r)).((-3)^(r))/(x^(3r))`
`=^(15)C_(r).((-3)^(r))/(2^(15-r)).x^(30-5r)`
Let 30-5r =- 25
`rArr " "-5r=-55`
`rArr" "r=11`
`:.` coefficient of `x^(-25)=^(15)C_(11).((-3)^(11))/(2^(4))`
`=(-12xx13xx14xx15)/(1xx2xx3xx4)xx(3^(11))/(16)`
`=-(1365)/(16)xx3^(11)`