Use the ratio test to determine whether a, converges, where a, is given in the n=1 following problems. State if the ratio test is inconclusive. 2º" (n!)' Σ п (Зп!) 322.

Q: 28. (Continuation of Exercise 27.) If E=1an converges, and if 1 > a, > 0 for all n, show that E=1 In…

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Q: Q4: Let X1, X2, ... be a sequance of a random sample from Uniform(0,1). Let Yn Prove that Yn…

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Q: Theorem 64. Let {pk}1 converge to point If y # x, then {pk}1 does not converge to y. x.

A: Given that sequence pkk=1∞ converges to point x.

Q: Write the first five terms of p_j= j/(j+1) and then prove p_j converges to 1. Be sure to explicitly…

A: We have to solve an inequality for apsilon and j.

Q: 6. Find the interval of convergence of -x* . Where p >0 is a fixed constant.

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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: Q4. If E a, converges and a, > 0 for all n, can anything be said about E2

A: Given that an is a positive term series and series an is convergent.   Here objective is to find…

Q: Ee whether or not fn converges uniformly nclusion. b) (0, 1)

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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: 6.3 Represent the function f(x) =,, using a power series and find the interval of convergence. 2 – x

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Q: For each n ≥ 1, let fn : R → R, fn(x) =nx/(n + x^2) Show that the sequence of functions {fn}n≥1…

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Q: Use |S – SN| < bN +1 to find the smallest value of N such that Sy approximates the value of the sum…

A: According to the given information, it is required to find the smallest value of N such that SN…

Q: If 0< by <1 for all k and , br converges, then , converges. Lk-1 %3D1 Select one: True O b. None of…

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Q: Identify two subsequences of ((−1)^n + 1/n) which converge to different limits. You should include…

A: Let the given sequence is Sn=-1n+1n We have to find two subsequences of given sequence that converge…

Q: 1. Find the Interval, Radius and Center of Convergence. n 2" n=0

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Q: 34. Assume that an+1/an converges to p = 4. -1 Does > an converge (assume that n=1 An # 0 for all…

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Q: Find the exact value that the sequence sin" 1 converges to. (Note that as usual, sin" x means (sin…

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Q: that (An) rges in babilit to A II ntains a further subsequence that converges a.e. to X. only if…

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Q: Use the Ratio test to determine convergence or divergence α. Σ n=l 8" n! 5" 5 n n=1 6.Σ b.

A: As per ratio test If limn→∞an+1an&lt;1 then the series ∑n=1∞an is convergent.If If limn→∞an+1an&gt;1…

Q: 1. For what values of p is O'dx?

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want…

Q: 4. Which comparison would show that dx converges? x + e*

A: According to the given information, it is required to tell which comparison would show that the…

Q: x +1 29. Find the values of x for which > converges. 4 n= a) x=tV3 only b) x=1 only c) -3V3 d) x

A: we have to find value of x

Q: 1 Use appropriate tests to determine if E(-1)"+1, converges. n* log(n) + n! n=1

A: use appropriate test to determine whether the series ∑n=1∞-1n+11n4logn+n! converges according to…

Q: 00 For which values of p does E converge? (n° +7)" n=1 (Use symbolic notation and fractions where…

A: Given problem:-