If the expansion `(x^(2)+(1)/(x^(3)))^(n)` is to contain and independent term, then what should be the vlaue of m ?

If the expansion `(x^(2)+(1)/(x^(3)))^(n)` is to contain and independe

1.	If the expansion `(x^(2)+(1)/(x^(3)))^(n)` is to contain and independent term, then what should be the vlaue of m ?
Answer» General term `T_(r+1)=""^(n)C_(r)x^(n-r)y^(r),"for"(x+y)^(n)` `rArr` general term of `(x^(2)+(1)/(x^(3)))"is" ""^(n)C_(r)x^(2n-2r)(1)/(x^(3r))=""^(n)C_(r)x^(2n-5r)` For a term to be indep3edent of `x,2n-5r` should be equal to zero. That is ,` 2n-5r=0` `rArrr=(2)/(5)n`, since r can take only integer values , n has to be a multiple of 5