(In(n))" 00 Find the value(s) of a such that 2 is convergent T2 Answer:

Q: Do the following sequences {a} converge or diverge? Justify your answers (a) an 3" (b) an - (-1)"/ñ…

A: Explanation of the answer is as follows

Q: (1) Suppose that (an) tends to infinity. (a) Suppose that (bn) tends to minus infinity. What can you…

A: Let's delve into a detailed step-by-step explanation: (a) Sequence ( (anbn) ) as ( n ) goes to…

Q: Determine whether each of the following sequences convergent, justify!, is (@) (X₁) where I : =…

A: (a) The given sequence is . Since  is a bounded sequence and .Then Hence the sequence  is…

Q: Entered DIV 0.25 At least one of the answers above is NOT correct. (a) The series Σ(An). Div n=1…

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Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

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Q: n+1 (-3)*1 3n n=1

A: Ratio test : Suppose we have a series ∑n=1∞ an then define  c=limn→∞ an+1an . If 0≤c<1 then the…

Q: Determine if converge or diverge using nth term and if converge find its limit

A: Finally, we can say that : The sequence an​=(−1)nn+1n​ diverges.The sequence an​=4n3n+n​​…

Q: Examine the convergence of ,where a>1. (log x)" +1

A: First I have told about Improper integral of first kind and then using it evaluate the given…

Q: 00 A student claims that converges because n= lim -15

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Q: 1 1. Let aj >> 0 and an+1 = 4 an + An Show that the sequence {an} is convergent and find its limit.

A: Limit of the converges sequence

Q: compute the 9-th convergent to √29.

A: We need to find the smallest positive integer solution to  or compute the  convergent to .We will…

Q: Determine of each point convergens or diverges: (-2)"(x-3)" (3) √(n+1) M=O

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Q: 00 Let r be a constant. Suppose ' converges to -1, then the sum of )r' is i-1 i-0

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Q: If xi 2, 3dn-1+ 3"n-2 show that {xn} is convergent. identify the limit.

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Q: 3-x -1 <x < 3

A: 63-x &lt; 1=&gt;  63-x &lt; 1=&gt; 63-x &lt; 1=&gt; 63-x×3-x  &lt;  1×3-x                   ∵ 3-x…

Q: Is the sum from n=1 to infinity of sin(n) convergent, conditionally convergent or divergent?

A: The problem is asking us to determine whether the infinite series ∑n=1∞sin(n) is convergent,…

Q: Suppose that the sequence {an} converges to a and that la| < 1. Prove that the sequence {(an)"}…

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Q: of sequence Ex: Evaluate The DFT of (n) = [1,0,0,1] nyo 3

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Q: 9) n+3"

A: Comparison test for series of positive terms states that, If an, bn are two series such that…

Q: Suppose SELECT ALL A) sometimes converges depending on the sequence, a(n) B) lim a(n) # 0 never…

A: Given that, limn→∞a(n)≠0 then we have to find ∑n=1∞a(n) is convergence or divergence or depends.

Q: B) > n! (4x – 6)" is convergent for x = n=1

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Q: Q1-A) Test the following sequence whether it is converging or diverging:- 2n 2. = [0.25m 2 ) ]…

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Q: (c) (#n) = (n cos“ ()), n e N. %3D 2 (d) (xn) = ((-1)" - n+1 n E N. %3D

A: To find the limit superior and limit inferior of each of the following sequences: xn=ncosnπ2, n∈N…

Q: (a) Let a, = 1 and ant √1+a, for all ne N. (i) Show that {a} is increasing and bounded above by 2.…

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Q: (b) Show that the following sequence is convergent: 1+ (-1)" n² Yn = √2+ (c) Show that (yn)neN is…

A: (b) The objective is to show that the sequence yn=2+1+(-1)nn2 is convergent (c) The objective is to…

Q: 2n+1 4. Use the definition to prove that ) converges.

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Q: The sequence a,=n sin 1 converges Select one: True OFalse

A: We have to check