In Exercises 23–36, use the formula for the sum of a geometric series to find the sum or state that the series diverges. 1 23. + 1 1 + +. 82 8 43 44 24. 45 + 1 54 55 -n 25. 26. E 7.(-3)" 11 n=3 5" n=2 27. E (;) 4 28. () n=-4 n=0

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Q: 6. a) Determine whether each series is convergent or divergent. Carefully explain your reasoning.…

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A: The general form of a geometric series is a+ar+ar2+ar3+...... , where a is  the initial term and r…

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A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Identify which geometric series converge. Give the sum of convergent series. 2 + 6 + 18 + 54 + . . .…

A: 2+6+18+54+........ It is a geometric series with, First term=a=2Common ratio=r=62=3

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Q: c) [ : Consider the series: 7-1+ 1 1 7 49 + i) Is the given series a geometric series? Explain. ii)…

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Q: In Exercises 99–102,verify that the Ratio Test is inconclusive for the p-series. see the equation…

A: Verify that the Ratio Test is inconclusive for the p-series.           ∑n=1∞1n0.05

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

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A: First calculate the common ratio of the given geometric series than find its value.

Q: Identify which geometric series converge. Give the sum of convergent series. 3 + 6 + 12 + 24 + . . .…

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Q: 9. Determine whether each series is convergent or divergent. State clearly which test you use,…

A: Solution: The objective is to determine whether the given series is convergent or divergent

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

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Q: infty 26. E n² – 1 n=2

A: Telescoping series is a series where all terms cancel out except for the first and the last term.

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A: Geometric series are series of the form

Q: 5. Determine if the series is convergent or divergent and justify your reasoning. (-6)2n n29n n=1

A: We have given series  ∑n=1∞-62nn29n We can write this again as ∑n=1∞-62nn29n=∑n=1∞36nn29n=∑n=1∞4nn2…

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A: {an} and {bn}  are both bounded as they are convergent.

Q: 6. a) Determine whether each series is convergent or divergent. Carefully explain your reasoning.…

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A: First term= a= 1 Common ratio= 2/3

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Q: 22 29 25 26 27 29 28 Which equation could be used to calculate the sum of the geometric series? 4…

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Q: 9. Determine whether each series is convergent or divergent. State clearly which test you use,…

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Q: 22-1 3°+2

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

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Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 24 3 4 + 1+…

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