If X1, Y1, are two positive unequal numbers and Xn = (xn- 1+ Yn – 1) and y, = Vx, – 1 Ya-1 V n 2 2. V n2 2. Prove that the sequences ( x, ) and (y, ) are monotonic and they converge to the same limit.

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A: Given - x1>1 and xn+1=2-1xn for n≥2 To prove - xn is convergent and also find its limit .

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A: Here we use basic limit property

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A: use the formula for radius of convergence for the

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A: Given statement is FALSE. I HAVE given a counter -example.

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Q: 1. For r < 1, define fn(x) = ²x. (a) Prove that for x < 1, k=1 ƒ(x) = lim_ƒn(x) = 84x x(1+x) (1-x)³…

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Q: Given f: [2, )IR, prove that fn (x) = けx" It, converger uni formly to f6)-o.

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Q: 4. Let (#1, y1) = (0,0) and let (n+1, Yn+1} = (2+ yn, 3 – Tn) for n > 1. Prove that (Cn, Yn) is a…

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A: Given that fn(x)=xn (a) Define, f(x)=0x∈[0,1)1x=1 Take fn(x)=1xn. We say that fn→f pointwise if…

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Q: If |fn(x)| < an for all x and Ln=1 an converges, prove tha En-1 fn(x) converges uniformly. n=1

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Q: find if diverges or converges. if converges, then find its limit cos² (8n) an where n 2 0 8n-1

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