Finding a term in a binomial expnasion

[Yaaaldi]

Homework Statement

Find the term in the expansion of (x-(2/x^2))^14 which is of the form constant/x.

The Attempt at a Solution

I have worked out the general expression. (14|r) x^14-r * (-2/x^2)^r

However I can only work out this problem by trial and error. I know that in this case r=5, however I didn't solve it by equation. What equation would I need to construct to get this answer r=5? I know that for the answer to be constant/x the power of x on the denominator can only be 1 greater than the power of x on the numerator.

How do I construct an equation with r to solve this?

Thanks

 

[Dick]

(-2)/(x^2)^r=(-2)/x^(2r). And, just as you said, 14-r should be one less than 2r. Can you set up the equation from there?

 

[Yaaaldi]

haha oh dear. bit of a facepalm moment.

14-r=2r-1

solve to get r=5

I never thought of just putting 2r-1.

Thanks for getting that out of me!