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Smitarani Swain posted an Question
December 27, 2021 • 19:09 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Cotvetget dna lim a, 2 ex cquehce (x,) is bounded and monotone where x - and x. = 2xn, then it conve to 2. observe that x > x,. since x x = 2(%, x,-1). by induc

COTveTget dna lim a, 2 Ex cquehce (X,) Is bounded and monotone where x - and x. = 2Xn, then it Conve to 2. Observe that x > x,. Since x X = 2(%, X,-1). by induction (x) is increasing. It can Sol observed again by induction that x, 2. Given x, = V2 Xna12x, Let lim x =l no then lim x-1 = lim 2x n0 n00 l= v2 2= 2 (2 2 = 0 e(l - 2) = 0 l = 0, 2 Since l> 0 l = 2

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