20. Show that if E-1a, converges, then 1 + sin(a,) Σ n=1 converges.

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Q: 8. Determine by the ratio test if 2n=1 (2n)! converges or diverges.

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Q: 2 then E " Cn+1 converges. 3.11 limnr+m

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Q: 7N 8N 3) Show that converges/diverges.

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Q: +o0 (-1)*n" sin" () Σ 2n n=1

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Q: 1 n4 + sin“ n=1

A: To find that the given deries diverges or converges

Q: Let {fn(x)} : „x ER and > 0. 1+ nx Show that ift>0, the sequence {fn(x)} converges uniformly on

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Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: 2) is E=1 2n convergent?

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Q: If 2 a, converges, then la,| diverges. n=1 n=1 True False

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

Q: 59. Show that 1- sin x dx converges. x? 00

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A: The objective is to show that fixed point iteration generated by the function gx=2x+53 converges in…

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Q: 99. Show that 00 cos x dx is absolutely convergent.

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Q: 5. (a) Suppose 1 and Xn+1 = 2 Show that {n} converges and find the limit. X1 for all nEN.

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Q: 1 Determine by the direct comparison test if Ln=1 2n+1 converges or diverges .

A: The given series is ∑n=1∞12n+1 We have to test the convergence

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Q: 3 If Xn 4 and ly,l0. Select one: True O False

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A: Sequence

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A: Note: since you have posted multiple questions. As per our guidelines we can solve only one problem…

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Q: 1 x converges 1 ex - e-X Select one: True False

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A: According to the given information, Suppose,

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A: Topic:- sequence and series

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Q: 7. Let x₁ = a > 0 and Xn+1 = x + 1/x,, for n E N. Determine whether (x,) converges or diverges.

A: Q7 asked and answered.

Q: 1 Show that the series 2 converges. k=2 k(log k)?

A: Given: ∑k=2∞1klogk2

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Q: 4) Show why the fixed-point iteration generated by the function g(x) = V2x + 5 converges in the…

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