# Math Help - Inequality!!

1. ## Inequality!!

If x1, x2,….., xn are positive numbers and n is a natural number, how do you prove that
(1+ x1)(1+ x2)…..(1+ xn) >= 1+ x1+ x2+…..+ xn

The only thing I can think of here is that ∏(1+xi) - ∑ xi >=1 , where i goes from 1 to n
Is induction required here?

2. Originally Posted by harish21
If x1, x2,….., xn are positive numbers and n is a natural number, how do you prove that
(1+ x1)(1+ x2)…..(1+ xn) >= 1+ x1+ x2+…..+ xn

The only thing I can think of here is that ∏(1+xi) - ∑ xi >=1 , where i goes from 1 to n
Is induction required here?
Yes induction is required :

for n=1 we have: $1+x_{1}\geq 1+x_{1}$

Now assume the inequality to hold for n=k and then prove it holds for n=k+1