n Σχ. X; - 1. show that i=1 converges in probability and finds its limit. E exp(2X;) 2. show that i=1 converges in probability and finds its limit.

Q: 3. Use the Test for Divergence to explain why if En-0 an converges, then En=0 am must diverge.

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Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: Given a statement if ∑n=0∞anxn and ∑n=0∞bnxn both converges at x=x1 the so does ∑n=0∞an+bnxn. To…

Q: et For which values of p does converge? (1 +e2*)P

A: Given:∑n=1∞ex1+e2xp

Q: Mark each statement True or False. Justify each answer. (a) If (sn) and (t„) are convergent…

A: Given:  (a) If sn and tn are convergent sequences with sn → s   ,  tn → t then limn→∞sn+tn=s+t and…

Q: 1 1 3. Find the sum of the following convergent series: 2" (п+1Xn+2)

A: As you didn't mention the question numberto be solved so i solved First  question.For remaining…

Q: Show that if Σ i=1 converges towards a € R , then lim ) a; = 0 i=N

A:

Q: Find F(s). F(s)

A: We use the table of Laplace transform to answer the given question.

Q: 3. Find the pointwise limit of 12 on S = [1, ∞o). Hint: Define L E R by L = 1/2 (L = 2 but you don't…

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Q: Are there value of fer which omy ĭ he converges.

A: A  series is said to be convergent if ad only if the sequence of partial sums of the series…

Q: 2. Show that if a > 0, then the sequence (n²a?e¬n*) coverges uniformly on the interval [a, ∞), but…

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Q: The limit of the sequence a,= (1+) s: (a) – e? (b) e) (c) e-a (a) e) (e) None

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Q: Let r be a constant. Suppose >,r i=1 converges to 8, then the sum of >r' is i=0 Answer:

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Q: 3 - If E is convergent, find its sum. z=1 en n(n+3)

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Q: 1. determine if it diverges or converges n e2n n=1

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Q: dx Determine if the improper interal S, xc Fnd it valne if it converges. Conneeges on diree jes.…

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Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

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Q: (a) (b) (c) +8 {√n+1 = √n+ 2 } 2 ONG e n=1 In n +00 n=1 n=1

A: First put 5 terms and find value and look at the limit as n is large.

Q: 24.6 Let fn(x) = (x − 1)² for x = [0, 1]. (a) Does the sequence (fn) converge pointwise on the set…

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Q: 3 z²+1 2. Find the area of the region in the first quadrant between the graph of y the z-axis. If…

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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: 23k-2 00 . Use the ratio test to determine if > 'k²3?k+1 converges or diverges. k=1

A: We have to find the given series is convergent or divergent by ratio test.

Q: If both E Un and E(-un) converges then E Un| n=1 n=1 n=1 is also convergent.

A: It is given that ∑n=1∞un and ∑n=1∞-un converges.

Q: n=1 n³ cos² n n²e²n + Inn

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Q: |6n cannot be evaluated directly. We will first find the limit of a related king the natural…

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Q: the ents 86. cheek the comvergenie g i) E sin (h ) - 3

A: (i) Given ∑sin1n Let un = sin1n Assume vn = 1n Consider limn→∞unvn = limn→∞sin1n1n= sin00= 00 Thus L…

Q: 2. If Exn and E yn are convergent. Show that E(xn + Yn) is convergent.

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Q: Let g(x) = E-o (-1)" (2n): Find the interval of convergence g.

A: We have given g(x).  We have to find the interval of convergence.

Q: lim- -po0(/ + a – 2)=? O a. 00 O b. 1/2 O .0 O d.Limit does not exist O e. 1

A: To find:            limx→∞x2 + x - x