I really dont know how to solve this problem.

Printable View

- Oct 2nd 2009, 08:05 AMsantiagos11an induction proof
I really dont know how to solve this problem.

- Oct 2nd 2009, 10:54 AMMr Smith
- Oct 2nd 2009, 09:17 PMmr fantastic
The attached question is: Use induction to prove that

$\displaystyle \frac{1}{n} \sum_{i = 1}^n x_i \geq \left( \prod_{i = 1}^n x_i \right)^{1/n}$

for positive integers $\displaystyle n$ and real numbers $\displaystyle x_i$. - Oct 5th 2009, 01:31 PMsantiagos11
I understand the proof for n=2^k, for k = 0,1,2,...that is for n = 1,2,4,8,...

But then how does one proceed to prove for n = 0,1,2,...