Consider certain real numbers ui and vi, i = 1,..., n, n <∞0. Show that (u₁v₁ + U₂v₂)² < (u² + u²) (v² + v²). Using mathematical induction, verify that athe following statements holds for any n < ∞0: |u₁v₁ + U₂v₂ + + UnVn] < (u² + u² + ... ·+u²/2)¹/² (v² + v²2 + +v2²2)¹/2 Explain how this leads to the Cauchy-Schwarz inequality: u. v ≤ uv, where u = (U₁, U2,..., Un) and v= = (v₁, V2,..., Un).

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