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steelphantom
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Homework Statement
Prove that ([tex]\sum_{j=1}^n[/tex]ajbj)2 <= ([tex]\sum_{j=1}^n[/tex]jaj2)([tex]\sum_{j=1}^n[/tex](1/j)bj2)
Homework Equations
Cauchy-Schwarz Inequality: |<u, v>| <= ||u||*||v||
The Attempt at a Solution
If I let u = [tex]\sum_{j=1}^n[/tex]jaj2 and v = [tex]\sum_{j=1}^n[/tex](1/j)bj2, then I have ||u|| = sqrt(<u, u>) and ||v|| = sqrt(<v, v>). Not really sure where to go from here. Any ideas? Thanks!