- #1
EighthGrader
- 11
- 0
Homework Statement
Prove the AM-HM inequality using the Cauchy-Schwarz Inequality.
Homework Equations
Cauchy Schwarz Inequality:
[tex]
\[ \biggl(\sum_{i=1}^{n}a_{i}b_{i}\biggr)^{2}\le\biggl(\sum_{i=1}^{n}a_{i}^{2}\biggr)\biggl(\sum_{i=1}^{n}b_{i}^{2}\biggr)\
[/tex]
AM-HM inequality:
[tex]A(n,a_i) = \frac{a_1 + a_2+\cdots+a_n}{n}\[/tex]
[tex]H(n,a_i) = \frac{n}{\frac{1}{a_1}+\frac{1}{a_2}+ \cdots+\frac{1}{a_n}}\[/tex]
[tex]A(k,x_i) \geq H(k,x_i)\[/tex]
The Attempt at a Solution
I just need some tips on how to approach this problem. How do I introduce the term [tex]n[/tex] on both sides?