Let be an irrational number. If for rational number (b≥1) 1 < a then 2b² prove that b is equal to one of the convergents of simple continued fraction expansion of Ę.

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A: Given,  is convergent, where, So,  is.Now, using A.M≥G.M property,We have,

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Q: Assume that the sequence shown below converges and find its limit. √3, √3+√3,√√3+√3+√3 √3+₁ " 3 +…

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Q: 3. Let: f(x) = In (1+x) a) Use four-digit rounding arithmetic to evaluate f(x) when x = 0.25. b)…

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Q: Show that X is complete if and only if every absolutely convergent series in X converges.

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Q: 6) Find the first five convergents of the simple continued fraction expansion of each real number.…

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Q: hat' H(x)= I ñ* ,x>1. (±) **9e グニン (a) Show that the series Convi unit on [a, as) where a> (b) Shaw…

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Q: ak Assume ak, br > 0 for all natural numbers k and lim k→o \ bk = L for some real number LE (0, 00)…

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