`((x^(2))/(2)-(3)/(x^(3)))^(15)` के प्रसार में `x^(-25)` का गुणांक ज्ञात कीजिए।

Explanation

`T_(r+1)=.^(15)C_(r)((x^(2))/(2))^(15-r)(-(3)/(x^(3)))^(r)`
`=.^(15)C_(r)*(x^(30-2r))/(2^(15-r))*((-3)^(r))/(x^(3r))`
`=.^(15)C_(r)*((-3)^(r))/(2^(15-r))*x^(30-5r)`
माना 30-5r=-25
`rArr-5r=-55`
`rArr r=11`
`thereforex^(-25)` का गुणांक `=.^(15)C_(11)*((-3)^(11))/(2^(4))`
`=(-12xx13xx14xx15)/(1xx2xx3xx4)xx(3^(11))/(16)`
`=-(1365)/(16)xx3^(11)`