EM8 Exercise 4o Consider the alternating series (-1) nor 1. Show that the series converges 2. Rearrange the serfes in such (show diver gence of the rearran ged series) a way that it diverges

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (– 1)*+1 10 k!…

A: Let us determine the convergence of the series in the next step.

Q: Determine whether the telescoping series converges or diverges. 5 5 Σn=1 (√2+2 -√2+3) /n+2 a) The…

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Q: 1 an 3sin2(n) The series converges. O The series diverges.

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Q: Detemine whether the series is absolutely Convergent fonditionally convegent, ordivergent. 2²+2n+3.…

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Q: 4. Determine whether or not the series converges. State which test you use. 00 n- 2n2 + 1 n=1

A: We have to Check whether given series is convergent or divergent by Root Test.

Q: Determine whether the series converges. k=1 The series

A: Ratio Test : Suppose ∑ak be an positive term series and                         limk→∞ ak+1ak =L ,…

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Q: Determine whether the series converges or diverges. n + 1 Σ n = 1 O converges O diverges

A: Solve the following

Q: Determine whether the alternating series £ (-1)n+1, n3 converges or diverges. n= 1

A: Given alternating series is  ∑n=1∞-1n+13nn3

Q: 1" n=1 V 2n +n– 1

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Q: Determine whether the series converges or diverges. +00 2n + 2 Vn3 + n² + n n=1

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Q: 3'

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Q: Determine whether the series converges or diverges. Indicate the type of series or test(s) that are…

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Q: By using Alternating series test,determine if the series converges or diverges: (-1)*+1 k+ 2

A: The series is  ∑k=1∞ (-1)k+1k+2

Q: Vn 2(-1)" п — 1 n n n=2

A: Alternating Series Test: Let unn∈Nbe a monotonic decreasing sequence of positive real numbers…

Q: the bot test to determine it the use tollowing series converges or diverges

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Q: oblem 5. Determine whether the series converges or diverges. (a) Eo(-5)"3–2n 5n-2 (b) En=1 ôn

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Q: Determine whether the alternating series 2(-1)^*' | - Σ converges or diverges. 13 n=1

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Q: Let an Does {4,} converge? Does a, converge? In +1 Give an example of a divergent seriesE, where lim…

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Q: 9. Use the alternating series test to determine whether 2(-1)"ne-" converges or diverges. n=1

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Q: Determine if the series is conditionally convergent, absolutely convergent or diverges. M-1)"- n =1…

A: The given series is: ∑n=1∞(-1)nnn3+4...(1) The absolute value series is: ∑n=1∞nn3+4 Let,…

Q: determine whether the geometric series converges or diverges. If a series converges, find its sum.

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergen 5(- 1)k+1 4k k=1…

A: Find your answer below

Q: Determine whether the series converges or diverges. 2n n = 1 2 + 5" converges O diverges

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Q: n° Use Ratio test to determine if the given series is convergent or divergent:

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Q: Determine if the series converges or diverges. W

A: Given: ∑n=1∞(-1)n10n(n+1)!

Q: Determine whether this series converges or diverges by p-series test. 1 n=1

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Q: By using Alternating series test,determine if the series converges or diverges: (-1)k–1 VE k=1

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Q: Determine whether the series converges or diverges. Vn4 + 3 n-1 n3 + n2 converges O diverges Submit…

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Q: Test the series whether convergent or divergent? 1+ 2" 1+ 3" n=1

A: The general term of the given series is: an=1+2n1+3n We shall calculate  L=limn→∞|an+1an|If L<1,…

Q: Given the series G) Does this series converge or diverge? O converges O diverges If the series…

A: The general term of the given series is  ak=14k This is a geometric series and we know that a…

Q: Determine whether the series converges or diverges. n2 - 4n n3 + 6n + 4 converges O diverges

A: Solution

Q: Determine whether the series is convergent or divergent (use Comparison Test). Σ 1 2+n3 n=1

A: We will determine whether the series is convergent or divergent as following.

Q: Determine if the series converges or diverges ( 2) Σ2

A: As per guideline we have to solve 1st one

Q: +oo (-1)"+1 n=1

A: To show the convergence using alternating series test.

Q: Determine whether the alternating series converges or diverges

A: Check whether the series is convergent or divergent.

Q: (b) Determine whether the alternating series converges or diverges by using the alternating series…

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Q: Determine if the series is convergent or divergent. Explain why. (8 pts.) 3*+1 n=0

A: Ratio test:

Q: n-1 Σ Given the series 8. n=1

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Q: By using Alternating series test,determine if the series converges or diverges: (-1)k+1 k + 2

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Q: Determine whether the series converges or diverges. Σ e2/n n = 1 O converges O diverges

A: Given series is, ∑n=1∞e2/nn

Q: Does the series converge or diverge?

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Q: Determine whether the series converges or diverges. n" n = 1 O converges O diverges

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Q: Determine

A: We have to determine the given series is converges or diverges

Q: Determine whether the series converges or diverges. 40n! Σ nn n = 1 converges O diverges

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Q: Determine whether the series converges or diverges. Σ n2 + 5 n = 1 converges O diverges

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Q: 00 Consider the series > a, where a, = (-1)*+7 In( 1 + - n n=1 Is the series (eventually)…

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Q: n! =) Use the ratio test to determine if the series converges or 100 diverges.

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Q: PART III Q5. Determine whether the following series converges absolutely, converges conditionally,…

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Q: Determine whether the series converges or diverges. Make sure to clearly state the test that you're…

A: Given,  ∑n=0∞2xnn!