Inequality calculus proof

  • Thread starter ~Sam~
  • Start date
  • #1
~Sam~
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0

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.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,223
31
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.
 
  • #3
blake knight
31
0

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.
 
  • #4
~Sam~
80
0
"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
 

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