Show by an example that Panbn may diverge even if Pan and Pbn both converge.

Q: |an also converges because 0 If an converges then < lan|, for n = 1, 2, ... n=1 n=1

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Q: Show how series is divergent

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Q: Discuss the Conditions foo which Foudies Segies is convergent?

A: Given: Conditions of Fourier series is convergent.

Q: 3* + 4* 2) What does converge to?

A: ∑k=1∞3k+4k5k

Q: converges, because 0 < 1 and an %3D debook 2n + 1 2n +1 2n +1 Room

A: We have to choose the true or false

Q: +o0 Σ)

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Q: D) { (-)"} [Select] [Select] converges to 2.

A: Please see the below picture for detailed solution.

Q: =1 nº+1

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Q: Prove that if a sequence  {an} converges, it must be bounded. Is the converse true as well

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Q: Show by example that Σ(an/bn) may diverge even though Σan and Σbn converge and no bn equals 0.

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Q: State why the following intergral is improper and find the value if it is convergent: 2r (z² – 4) "

A: The given integral is I=∫262xx2-423dx The integral is improper as the integrand is unbounded at x=2.

Q: Find the limit numbek of the fallawing Sequencer er divergente and which of them is convergent 4-…

A: To find the convergence of the sequence and obtaining the limit

Q: Which converge and diverge?

A: In this question, we have given four multivariable functions. for each of them, we have to check the…

Q: Determine whether the following is convergent or divergent and justify

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Q: 2n + 5 9n + 4 n=1

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Q: 21.) Converge or diverge? Explain. En=1 3n - п!

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Q: Test the convergency o f Stan ("

A: According to the given information, it is required to test the convergence.

Q: 1 3 .5 4 X +x

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Q: An example of: Σ(an/bn) may diverge even though Σan and Σbn converge (show each step please)?

A: We have to show that Σ(an/bn) may diverge even though Σan and Σbn converge

Q: converges or diverges. I-

A: We have to find out the given series is convergent or divergent. If the series is convergent then we…

Q: 8. 27 n=3

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Q: 1 3. En=1 (2n+1)3

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Q: Determine if the following converge or diverge.

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Q: If an| converges then diverges because for large n. Vn n=1 True False Reset Selection

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Q: Corver Is absdutely contergent, Conditionally Convergent, on divergent

A: Use Alternating series test, P- series test

Q: Show that every convergent seapuence is Cauchy but the convesse is not true in general.

A: A sequence is said to be Cauchy if there exist a natural number N and a small positive number such…

Q: If an> 0 and Σ an converges, then Σ(-1)"an converges.

A: We have to check wheather it is true or not

Q: 2 – 5n 11п-1 n=1

A: Use ratio test.

Q: 3と 2. (1) 7k tel

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Q: Let ³ 10n 4n + 1 Determine whether is convergent.

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Q: Does 1/201+1/208+1/227+1/264+... converge or diverge and why?

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Q: 1 -2 (x+1)²

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Q: 13 3.7 3.7.11

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Q: + 4* 2) What does converge to?

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Q: Determine whether the statement is true or false. dr is convergent.

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Q: (a) Determine whether {an} is convergent.

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Q: converge to the same limit.

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Q: Evaluate V4 – x²dx if it converges.

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Q: /5 too dr Vx-1

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Q: converges, because lim n! 2(n+1) n! = 0. (n + 1)! 2* n+00 True False Reset Selection

A: The given statement is true. Use the ratio test to find the evaluate the nth term.…

Q: =) Show that converges/diverges n-1

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Q: test the convergehce and clivergence 2'coscnt)

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Q: By 6/2silon definition, check the convergenie of fallowing sequenres. the =

A: We have to check the convergence of the sequence by using the epsilon definition…

Q: Show that 2"x" converges if |x| <. n=1

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Q: Determine if the following is convergent or divergent: a dr

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Q: • Determine if √2 + √₂-√2 + √2-√2+√² + √2-√2+√2,75 Converges diverges. or

A: What is Infinite Series: Infinite series is the sum of terms of an sequence starting from n=1. As…

Q: Determine whether (an + bn) is convergent or divergent. n=1

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Q: 1 3.

A: According to definite integral formula ∫acf(x) dx=∫abf(x) dx+∫bcf(x) dx . According to power rule of…

Q: 3k 5- 2k+1 k=1 2 1. Does converge? If so, what does it converge to? If not, justify.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.