prove by definition 3/n and 1/n^2 converges to 0.

Q: Calculate whether it is convergent or divergent. (4x)2* x=1

A: Given series is ∑x=1∞(4x)2xexx2x

Q: Wi n=1 (-2)^ n! n^

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Q: p for which In (n) Comvenges

A: Given∑n=1∞ln(n)np

Q: Use the root test to determine whether convergent or divergent from k=1 and ♾ of (9k+2/16k+1)^-k/2

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Q: Can you further solve how exactly to find a convergent subsequence here?

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Q: 2 ทะ n (8) n! h

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Q: 1 n=2 n(Inn)P -4

A: We need to find the value of p for which series convergent.

Q: Show that if a>-1 and b>a+1 , then the followingintegral is convergent.

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Q: 2) is E=1 2n convergent?

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Q: Š V2n-5 n=1 n2- 3n +4

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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: з Σ (-1)^ hai боu итиеть n ди

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Q: Does the infinite series O It converges. O We don't know. 10++ + 10 53/2 + converge or diverge?

A: Please see the below picture for detailed solution.

Q: Let a (> 1) be an irrational number. Show that the kth convergent of the simple continued fraction…

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Q: How do I determine if this converges to a certain value, or diverges without bound?

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Q: Determine whether aedx is convergent or divergent.

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Q: Prove 2^1/n infinity n=1 is convergent

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Q: finding if this converges or diverges

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Q: Let fn(x) = x/(n^2+x^2) for x ∈ R. Show that the sequence {fn} converges uniformly to the function…

A: Solution:  Let  fn(x)=xx2+n2,for  x∈ℝ   and  n∈ℕ For  x=0, we  have  fn(0)=0⇒limn→∞ fn(0)=0⇒limn→∞…

Q: Se ทะเ Ifu ^^ +2 2

A: To find whether the series is absolutely convergent or not.