(b) Prove that inf{1⁄2 − ² | n,m € N} = −3. Start by stating the definition of the infimum. m [4] A4. (a) Suppose that (x) is a sequence of real numbers. Define what it means to say that the sequence converges to 0. [4] (b) Prove from the definition of a limit that the sequence (xn) with n= √n converges to 0. [4]

Q: Consider the following differential equation. (2x - 1) dx + (7y + 5) dy = 0 Let M = 2x - 1 and N =…

A: Let M=2x-1 and N=7y+5   My=∂M∂y=0Nx=∂N∂x=0 Here My = Nx hence the given equation is EXACT…

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A: Finally, we can say that : The sequence an​=(−1)nn+1n​ diverges.The sequence an​=4n3n+n​​…

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Q: Determine if the following sequences converge or diverge. You must justify your answers. If they…

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Q: Consider the sequence defined by æo = 1 and for n > 0, an+1 = v2 . xn (a) Is this an implicit or…

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Q: help with this hw problem

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A: This question is related to sequence and series.

Q: Exercise 2.4.3. (a) Show that V2, y2 + v2, V2+ V2 + v2,... converges and find the limit. (b) Does…

A: (a) Given sequence is 2, 2+2, 2+2+2,..... We have to show that the sequence 2, 2+2, 2+2+2,..... is…

Q: 1) In order to use the integral test, we must verify that the sequence is decreasing (and positive…

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Q: Prove that the sequence is monotone and bounded. Then find its limit. s1 = 5 and sn+1 = V4sn +1 for…

A: See the attachment

Q: 5. Use the definition of convergence to prove that the sequence (sn) diverges where Sn = √n.

A:

Q: 2. Let the sequence (n) be recursively defined by x1 = √√2 and xn+1 = √2+xn, n≥1. Show that (xn)…

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Q: 5. Show that the infinite sequence a, = Vn2 + 1 – yn² – 1 (n 1) converges by showing that it is…

A: Given sequence is  an= √(n^2+1) - √(n^2-1)