Question 72469
In the binomial expansion of {{{(a+b)^n}}} the r-th term is given by {{{nC[r]a^(n-r)b^r}}} when 'n' is a positive integer.

Here, {{{a = 2x}}}, {{{b = -2/5x^2}}}, {{{n = 8}}}.

Hence, the r-th term is 
{{{8C[r](2x)^(8-r)(-2/5x^2)^r}}}
= {{{(-1)^r 8C[r](2^(8-r)(2/5)^r)x^(8-r)x^(-2r)}}}


Thus constant term is that one for which power of x is zero i.e. 8 - 3r = 0.
This gives r = 8/3. But r should be integer.
So you are correct!
This binomial expansion doesn't have a constant term if you have typed correctly.