## Question

###### Prove thie following lemia: Lerma Let {Ta}i sequence of real nurnbers We define C) new sequences {E,k_] and {O-}=1 Vn â‚¬ 2+ I Vn â‚¬ 2 Tin-1IF the scquenees (E,} =1and {O};=1 #re both convergent tothe same litnit, THEN the scquence {Ia}i 1 also convergent: Suygeston: Use the definition o Iitit,

Prove thie following lemia: Lerma Let {Ta}i sequence of real nurnbers We define C) new sequences {E,k_] and {O-}=1 Vn â‚¬ 2+ I Vn â‚¬ 2 Tin-1 IF the scquenees (E,} =1and {O};=1 #re both convergent tothe same litnit, THEN the scquence {Ia}i 1 also convergent: Suygeston: Use the definition o Iitit,

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