converges for all * > 0 because lim a - In n 0, for all * > 0- n=2 True False

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A: We have to find the option

Q: converges to 0 Select one: True False

A:

Q: By using integral test show that the series 1 is convergent to 4 [en+e-nj² n=0

A:

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A:

Q: converge absolutely, non-absolutel

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Q: 11.) -1 n=1

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Q: Jse series to evaluate the limit. 323 sin(4x) – 4x + lim

A: We have to find

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A:

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Q: this series is ans. absolute convergent for x < divergent at x=0 none of these conditional…

A: I will use radius of power series and alternating series test.

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A:

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A: The radius of convergence is half of the length of the interval of convergence. If the radius of…

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A: To find the interval of convergence.

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A: Ad per our guidelines, I can answer only one question. To know rest, pleasere upload particular…

Q: 5. Use the Monotonic Convergence Theorem to show that x, converges. (부) -

A:

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Q: Show that Sum of two uniform'y Convergent sevuence uniformiy Converg ent ? is

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 2(-1)n - 1_3" 2"n3 n…

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Q: Prove that or 「+ X。- ズー 2. 71 number J2 Converged to

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Q: an conditionally converges then Jan] converges. n=1 n=1 True OFalse Rationale: Reset Selection

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

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A:

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A: The given power series is                            ∑n∈ℕnnn!zn We know that if R be the radius of…

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Q: Find the radius of converyence and interval of convergenc (11)

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Q: The radius of convergence of -2 (x+6)" is: n=1 (-5) " (n)

A: Radius of convergence is calculated as below, The correct answer is option 2 i.e., 5

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A: if integral is finite then series is convergent

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

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A: We have given the series

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A:

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A: this is inconclusive because if it converges for x=2 than  converges only the values less than 2 but…

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A: The question is solved by monotone convergence theorem. The sequence is decreasing and bounded below…

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A:

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.