if the term independent of x in the expansion of (ax-1/x^2)^6 is 240,find a

In case of binomial expansion of (a+b)ⁿ, it is written as

ⁿC₀aⁿ+ⁿC₁a^n-1b+......+ⁿC_nbⁿ

So, for the given expression, the term ⁶C₄ will have ax⁴ and 1/x⁴. So

it will be independent of x.

So, ⁶C₄a⁴=240

Or,

 

a⁴  =6! / 4!2!240

a⁴  = 15/240

a⁴  = 1/16

 

So, a = 1/2