n! 4 · 9 · 14 · .· (5n – 1)* n=1

Q: n n² 2" . Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does…

A: the objective is to evaluate the limit and tell about the series using the ratio test.

Q: 1001 an bn converges and lim no b, lem 5. Let {a„} and {b,} each be a sequence of positive real…

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Q: Determin tollowing series Convergence divergence. or り It zU

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Σ (). 4 4 n=D0 O Diverges by the Divergence Test (nth term test). O Convergent Geometric series. O…

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Q: -) True or False. A series an always converges if lim,0an = 0. If true give reasen, %3D n=1 if false…

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Q: these are the choices

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Q: Consider the series а, where a, %3 5 1+- n n=9 Compute the limit: lim yan = n00 (Enter "infinity" or…

A: Follow the steps carefully to solve the problem.

Q: (i) Let an Σ n cos A. Which test should be used? (enter upper case DCT for direct comparison test or…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: (In n)2 5. an = 6. bn T = n sin Hint: Look for a way to use L'Hopital's Rule -

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Q: If the series En=1 an converges absolutely, the sequence {b,} is bounded, then the series sin(a,)b,…

A: ∑ann=1∞ is absolutely convergent and bn is bounded .

Q: 3" + 5" We would like to apply the Limit Comparison Test (Part 1) on the series 4" + 7" Which of the…

A: We have to find which series should we compare the given series to.

Q: Consider the series Answer: L = n=1 (-1)" 7² Evaluate the the following limit. If it is infinite,…

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Q: 2n 5n – 1 Consider the series Evaluate the the following limit. If it is infinite, type "infinity"…

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Q: 18. Find a power series representation for the function and determine its interval of convergence a)…

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Q: Use test of coarse divergence to show divergenceof the series.

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Q: If you are using the Limit Comparison Test and the limit is 1. your conclusion is that O The unknown…

A: According to question if you are using the limit comparison test And the limit is 1 your conclusion…

Q: Using only power series techniques and algebra, evaluate the following limit. lim      ( 1-e^ax) /…

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Q: 25.) The p-series (a) diverges if ps1 (b) diverges ifp1 (e) None of these

A: Given: ∑n=1∞1np

Q: > an where a,, = In n Consider the series n=8 Compute the limit: an+1 lim (Enter "infinity" or "inf"…

A: apply ratio test

Q: a1 = V6 V v6 a2 = 6 + az = V 6+ y6+ v6 /6+ võ a4 = 6+ V 6+ V6 + v6 a) Find a recursive formula for…

A: Follow next step

Q: Consider the series -)*"*S" . Evaluate the the following limit. If it is n! n=1 infinite, type…

A: Since you have posted multiple questions as per our policy we will answer first question. Please…

Q: Determine the convergence or divergence of the sequence (not series!) with the given nth term. If…

A: Check the convergence of the sequence with nth term an=ln n2n.

Q: Consider the series Suppose T-1. lim ky00 TL1 (2₁(-1²) CT CH() X Hint: Consider what happens if k is…

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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: 8. a. What is the power series reprsentation for centered at x = 0? Here, just %3D 1-x an answer is…

A: The power series expansion for fx=11-x is in the form ∑n=0∞xn That is: 1+x+x2+x3+........ Therefore,…