Use the Raho Test to determine whethen the serics is convergen Or dveraent 2.

Q: Show that the sequence {f}, where f₁²x) = tan `nx, x70 is uniformly ノ on any interval [a,b], aso but…

A: Given function as fnx=tan-1nx, x≥0

Q: Find the Value of p which intagral the Converges, abso leste ly Cosn du- Conditionaly. to Jean de

A: Comment: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Show that x, converges to x.

A: Given that X be a metric space . Let xn be the sequence in a metric space X. Suppose that xn has a…

Q: Find the interval of convergence for the following power scries: (Зг — 2)" WI

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Q: Suppose that the radius of convergence of the power serles C.X is R. What is the radius of…

A: Given Radius of convergence of ∑cnxn   is R Thus,limn→∞cncn+1 = R

Q: * Show that the sequence (xn)n>1 in R, where In = 1- Vn' converges to 1.

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Q: the following saries is absolutely Conditionaly converge check iP Conv. or divergent そ(-1) (a!)?…

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Q: . If [an is a senies of pobitive terms md [an is convergent then cheek the convergenie of the…

A: Comparison test : If 0≤yn≤xn for n≥k for some k .Then  If ∑n≥1xn is convergent then ∑n≥1yn is also…

Q: If E lan| converges then Ean converges. Select one: O True O False

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Q: 00 1 n2 + 2n n=1

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Q: Use the Bolzano-Weierstrass Theorem to show that (Xn) = (1, 3, 5, 7, 1, 3, 5, 7, 1, 3,5, 7, . ....)…

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Q: 27 81 2) 16 – 12 + 9 – + 4 16 243 + 64 - - -

A: Given the series: 16-12+9-274+8116-24364+............ To check if the given series is convergent or…

Q: is it kue that if Can) and Cbn) two sequences of real humbers such Hhat : ansbu for all -nE N i aud…

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Q: Prove that {x_n} converges. Need to use info in a) and b)

A: We have the following information from part(a) and part(b) for any a,b∈ℝ…

Q: Use the Integral Test to determine whether the seriesconverge or diverge. Be sure to check that the…

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Q: Apply the Roio Test OR diver GeNT. CONverGe NT 8. 5h

A: Given query is to find series converges or diverges using ratio test.

Q: 00 1 n=2 un -1

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Q: Show that an abbolately converget sover ss mvergentserer es Condegent but Converse es not true în…

A: To show that if a series is absolutely convergent than it is convergent but converse need not be…

Q: If o an is convergente then o nan is divergente Select one: O True O False

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Q: 3. Use a Comparison Test to determine whether the scrics converges or diverges. State the name(s) of…

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Q: Use the limit comparison test to find the sum from k=1 to infinity of: [(5sin2k)/k!]

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Q: Converge or diverge with what test?

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Q: ) Prove that if XnXnand YnYn are any two sequences of real numbers such that XnXn converges to xx…

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Q: Prove for uniform covergence the series 1 „VxeR. (By using Weierstass's M-test). 5 7 2 n=1 n" +n'x?

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Q: Find the smallest positive integer n so that S, approximates the sum of the convergent ser to four…

A: Here we have to find the smallest positive integer n so so the Sn, approximates the sum of the…

Q: Hiw.which ef thefellowing serier which conditiunally converge absolutely converge and

A: Find the sum of the series.

Q: . Use the inegral test to show that =1 converges. 1+n2

A: To solve this question first we check derivative of function is negative for n>0 and then we show…

Q: krge, Absolutely coverge or conditionally converge? ntl (1) n+3 °

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Q: Test the convergence and ergence of the following ser h+ 2 in

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Q: ) Pick your favourite real power series o a,r". Show that for this series, the equivalence 00 Σ anx"…

A: c) Take an=1n!. Then the series ∑n=0∞anxn=∑n=0∞xnn! and ∑n=1∞nanxn-1=∑n=1∞xn-1n-1!. To show that it…

Q: n2 +1

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Q: Use the Root Test to determine the convergence or divergence of the ser 10) E: (In n)" n=2

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Q: Use the Raho Test to determine whether thc serics is convergen Or divergent oo(-3 n 0

A: Here, the general term of series  an is shown on board. Forstly, we calculate next term and…

Q: Test the llawing Seri es for being diverge Converge そ ) n +2 (-1) 30-1 (en)!

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Q: Use integral test to detrmine ; converge or diverge n n=1 Vn²+1

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Q: The integral S x3 converges to Select one: O True False

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Q: Show that the sequence ffn}, where fnox) = ne is uniformly convergent nx+1 on [a, b], aso but is…

A: Given: fnx=nxnx+1 To show that the given sequence is uniformly convergent on a,b, a>0

Q: Does the following senes. convege or diverge? N=1 Doos its @ sories divarges by Otegral test? b…

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Q: Find the limit of the sequence, using L'Hôpital's rule when appropriate. Vn Vn + 5

A: let I be limn→∞nn+5 Recall: limx→afxb=limx→afxb

Q: The Ratio Test can be used to determine whether O True O False converges.

A: Given ∑1n3

Q: If Ea, converges absolutely, prove that Ea,² converges.

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Q: Does a(n)= n^2sin(3/n^2) converge?  If so, to where

A: The given question can be solved as shown in step2.

Q: 8. Use the integral test to determine if IM8 k² (k³ + 2)3/2 converges.

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Q: Prove that the follo wing series is convergent for all reR sin Inc) n n=1 CS CamScanner ile tarandı

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Q: 8. sing the Ratio Test, check the convergence of the following eries: n(3n + 5) 8" (n + 2) In(2n +…

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Q: If 21ak converges then E,ak, converges for any ak subsequence of ak.

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Q: Show that Seauence Converse is not tade in gehQlali every Convergent is čauchy But

A: We need to prove that every Convergent sequence is Cauchy but the converse is not true

Q: ) Find all velyes of se for which the Senies 5o g Series n=0 Converges. use interval netation n…

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