1 1 = 0. Vn – 1+ /n converges because lim Vn – 1+ n n=1 True False

Q: can anything be said about E- an

A: Given that, ∑nan converges.

Q: Compute the limits of the sequences sin (n² – 3n + 7) n² +1 | 2n? +п -5 (b) b, (c) c, = n°e (а) а,…

A:

Q: 1 E(-1)"+1, ( n + 1 ) . 3η n=1

A: To find whether converges or diverges

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A:

Q: 5n 9. Use the L'Hopital's rule to determine if the sequence an = () converges or diverges as limit n…

A:

Q: Prove that limx-c f(x) = co if and only if for every sequence an that is in the domain of f and…

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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: uppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given…

A:

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: 5. Consider the equation f(x) = x - 2- = 0. (a) Show that the above equation has a solution on the…

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Q: (x + n)² Show that h„(x) converges poimtwise to f(x) = 1, V x e [1, 00). %3| x² + n²

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Q: (1) E(-1)n+1 (3n)! 3n+1 n=1

A: (f). Given series is ∑n=1+∞(-1)n+1(3n)!3n+1

Q: Match the sequence with it's limit as n- 00 2n+1 A. 00 3n2+2 В. О n! C. 2 D. 2 (n-1)! v 2n+2 3n+1 (-…

A:

Q: advanced MATH   Suppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is,…

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Q: Find the limit if the sequence converges and lim sup and lim inf if the sequences diverges (c and d)

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Q: (x – 5)" - 10. Determine the interval of convergence of n2 n=1

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Q: (-1)"-1 (In n)" 00 23. E n=2

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Q: Prove that the sequence xn has a convergent subsequence. 3n4 sin n – 4n cos n2 + 2 a) Xn 5n4 – 8n –…

A: We have to prove that xn has a convergent subsequence in each of the given cases.

Q: 3n3-2n2+4 6. Determine by the limit comparison test if Ln= n=D1 converges or diverges. n7-n3+2

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Q: 5a) Show that the sequence (Sn) given by s₁ = 0 and, for n ≥ 1 Sn+1 = √Sn + 2 converges and find its…

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Q: Find the limit (as n → ∞) of the sequence an = In(2n² + 5) – In(5n² + 2), n > 1. %3D

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Q: ? 4. Show that the sequence {fn}, where nx fn(x) = XER 1+n²x²⁹ is point-wise convergent but is not…

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Q: re 1. (a) Let fn(x) = (1-x)x". Prove that the sequence converges point-wise on [0,1]. Find the limit…

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Q: 1. Let (n) be an increasing sequence of positive real numbers and define the sequence (yn) as…

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Q: If X1, Y1, are two positive unequal numbers and Xn = (xn– 1+ Yn – 1) and y,= Vx – 1 Yn –1 V n 2 2.…

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Q: (a) Prove that (2x + 2) > 1 for all x > 0. (b) Let so > 0, and sn+1= } (2s, + ) for all n > 0. Prove…

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Q: Match each of the following with the correct statement. C stands for Convergent, D stands for…

A: Concept used: Divergence: When the values goes to -∞ or goes to ∞ that is it does not approach one…

Q: If P(x) is some polynomial then ΣP(n)x" has radius of convergence 1. n=1 Select one: O True O False

A:

Q: +00 (2n)! E(-1)"- 2" n=1 O divergent O convergent

A: The objective is to find the convergence or divergence of the series.

Q: 1 Σ 8n2 – 16n + 6 n=1

A: We will use limit form of comparison test to determine whether given series is convergent or…

Q: Exercise 2.4.3. (a) Show that V2, y2 + v2, V2+ V2 + v2,... converges and find the limit. (b) Does…

A: (a) Given sequence is 2, 2+2, 2+2+2,..... We have to show that the sequence 2, 2+2, 2+2+2,..... is…

Q: For eksample Xn = n² (n+1)! investigate whether the serles Σ 8 n=1 Xn convergent Or divergent. Prove…

A: We will use ratio test to check whether given series is convergent or not.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.