If a and y are positive real numbers, which of the following conditions guarantees that the infinite series B C *>y I> y² x

Q: Show that the series sin2x+sin4x+sin6x+... converges to tan2x if x≠(π/2)+nπ

A: Here I am attaching image so that you understand each and every step.

Q: Find the interval of convergence and the radius of convergence for each series.

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Q: Let x0, x1,x2,... be the sequence such that xo = 1 and for n ≥ 0, Xn+1 = ln(en — Xn) (as usual, the…

A: Let x0, x1, x2, ...... be the sequence such that x0=1. For n≥0, xn+1=lnexn-xn. We need to show that…

Q: Find the largest interval (in x) where the series summation from n = 1 to infinite of xe-nx…

A: Here we use D'Almbert ratio test.

Q: 8 1. Let an be a POSITIVE infinite series (i.e. an> 0 for all n ≥ 1). Let f be a continuous function…

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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: Find the interval of convergence and the radius of convergence for each series.

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Q: b) Suppose (xn) does not converge to 0. Then there exists e > 0 such that all except for finitely…

A: Let us suppose the following sequence xn=1,0,1,0,1,0,..... We have to see that the odd terms are 1…

Q: Solve Σ 0 to ∞ ((n! • x^n)/ n^n) for x = e and x = -e and explain whether each point converges or…

A: Solve for x = e and check whether it converges or diverges as follows.

Q: 00 Let r be a constant. Suppose ' converges to -1, then the sum of )r' is i-1 i-0

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Q: S sin(n) cos(n)/n converges or 3. Use to sandwich/squeeze theorem to argue whether the sequence 1+n…

A: We need to find if series converges or diverges.

Q: Suppose (xn) does not converge to 0. Then there exists e>0 such that all except for finitely many…

A: Consider the sequence xn=1,0,1,0,1,0,....... Here the odd terms are 1 and the even terms are 0.…

Q: For which z's does the infinite series 1+ 좋 + + +. zn + . 3" 27 converge? To what function does it…

A: The solution are next step

Q: 9. Prove that if {fn(x)} converges uniformly to the function f(x) on each of the sets A1, A2, ...,…

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Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

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Q: a, > 0 and Ea, converges, then (-1)"an converges O False O True

A: This is Not True. Hence False is the correct answer. We will prove this by taking an example, Let…