How Does (1+x)^r Compare to 1+rx for 0<r<1 and Specific x Values?

[~Sam~]

Homework Statement

Let 0< r <1. If x>0 or -1 less than or equal x <0. SHOW THAT (1+x) ^ r <1+rx

Homework Equations

no relevant equations

The Attempt at a Solution

I've tried isolating, but I can't relate x to x or r to r. I can't split the equation because I don't know r.

 

[rock.freak667]

Try using the binomial theorem to expand (1+x)^r and then think about what 0<r<1 and -1≤x<0 really means for your expansion.

 

[blake knight]

Homework Statement

Let 0< r <1. If x>0 or -1 less than or equal x <0. SHOW THAT (1+x) ^ r <1+rx

Homework Equations

no relevant equations

The Attempt at a Solution

I've tried isolating, but I can't relate x to x or r to r. I can't split the equation because I don't know r.

"If x>0 or -1 less than or equal x <0."--->I think this statement has some problem.

 

[~Sam~]

"If x>0 or -1 less than or equal x <0."--->I think this statement has some problem.

No there is no problem, it's X > 0 OR