Prove that or 「+ X。- ズー 2. 71 number J2 Converged to

Q: (b) Prove that the real power series n!r" converges for only r 0. %3D

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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: oblem 3. Use the integral test to determine whether Y converges or diverges.

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Q: 49. n=1

A: We have to check

Q: Show that the interval of convergence is (-o, +00).

A: The given question is related with interval of convergence. Given that fx = ex. We have to show that…

Q: 8.) Find the interval of convergence for Š 46x-3)" n=2 n² 2^ (Hint: Use Root rest.)

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Q: converge absolutely, non-absolutel

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Q: Prove that or quari -1+ X.- ズい 2. X. ntl converged number Ja to 2.

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Q: Find the interval of convergence of Σ 6" (2n + 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: Find the interval of convergence : En-0 (x-3)"

A: Apply ratio test to find the interval of convergence. When L<1 then series converges and When…

Q: if Xn is bounded, is Xn  cauchy ?  is Xn convergent?

A: Solution

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: State why the following intergral is improper and find the value if it is convergent: 2r (z² – 4) "

A: The given integral is I=∫262xx2-423dx The integral is improper as the integrand is unbounded at x=2.

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: 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: What are all of the values of x ,such that - (-1) n+A converges? n=1 .1 X26 .2 06

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Q: (b) Give an example to show that the product (fngn) may not converge uniformly.

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Q: Prove that if Ean converges , then (antanti+ --- anor)=0, Does it imply that Ean converges? Give…

A: Given: to prove, limn→∞an+an+1+.....an+r=0,r≥0

Q: ® Investigate the conurgence of 3. Convergence 2.

A: The given expression is ∑n=1∞n!2en2. We have to find whether the given series is convergent or…

Q: Determine whether sec(0)de converges and, if

A: Topic:- application of integration

Q: Find the interval of convergence of ) n°x" and find its sum. n=1

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Q: Use the Limit Comparison Test to determine whether converges or diverges. Vnvn +1 n=1

A: we have to test whether the given series is convergent or divergent by limit comparison test

Q: Corver Is absdutely contergent, Conditionally Convergent, on divergent

A: Use Alternating series test, P- series test

Q: 8n Show that fn (x) = x2" – x" is unfiormly converges or not by using uniform norm

A: The given function is  fn(x)=x2n-x8n We show that the function is uniformly converges or not by…

Q: #2. Give a counter exa mple that (Sn) is bounded but not convergent.

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Q: Show that every convergent seapuence is Cauchy but the convesse is not true in general.

A: A sequence is said to be Cauchy if there exist a natural number N and a small positive number such…

Q: Check the convergence of J (x-2)²

A: Let x-2=tThen dx=dti.e.∫-∞11(x-2)2dx∫-∞-11t2dt      [x=-∞, t=-∞-2=-∞]  [When x=1, t=1-2=-1]

Q: Prove that 「+ X,- ズー 2. 71 ,nyo converged number J2 ヒo

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Q: Prove, using the formal definition of convergence, that the sequence VnIni converges to 0.

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Q: Determine the interval of convergence of n=1 (x - 5)" n²

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Q: (т — 3)" - Determine the interval of convergence of 2n +1

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Q: Determine the interval of convergence of >, (-5)" (х — 3)" n2 n=1

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Q: 5. Use the Monotonic Convergence Theorem to show that x, converges. (부) -

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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: 3- a- By definition show that (x,) = (+3) converges to 3. b- Does (+3) bounded, Cauchy? Show by part…

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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: Let (rn) be a sequence of real numbers. Show that the convergence of (sn) implies theconvergence of…

A: We have to prove that if convergence of (sn) implies the convergence of (|sn|).

Q: 27 n! n=0 converges to 0. 8.

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Q: If \( \{a_n\}\)  is decreasing and bounded below then it is convergent.  true or false?

A: Monotone Convergence Theorem : Every bounded monotone sequence is convergent.

Q: (1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are…

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Q: .Use the Monotone Convergence Theorem to show that the (2n)! {a)" is convergent.

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Q: Suppose {a,} is monotonic. Prove that {an} converges if and only if {a} converges

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Q: =) Show that converges/diverges n-1

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Q: Show that 2"x" converges if |x| <. n=1

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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