You delete a finite number of terms from a divergent series. Will the new series still diverge? Explain your reasoning.

Q: Besides geometric series, what other convergent and divergent series do you know?

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Q: Find the sum of the series if possible, if not possible explain why: 3 (금)' + (금) -2 1+ 5 +...

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Q: What is meant by the sum of a convergent infinite series?

A: An infinite series is said to be convergent if the sequence of nth partial sums is convergent and…

Q: What test is advisable if a series involves a factorial term?

A: Let the series involves a fractional term ,

Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find its…

A: The given geometric series is 5+4+165+6425+⋯. Here, the first term is a0=5. Evaluate r as follows.…

Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find the…

A: The given geometric series is ∑n=1∞-7n-19n. Geometric series test: A geometric series ∑n=1∞arn-1 is…

Q: 3 п Σ 24 n=1 n* + 4

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Q: What is meant by the sum of an infinite series?

A: Explanation: If the number of element in the series is infinite then, the series known as infinite…

Q: -3 1=と

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Q: Find the sum of the arithematic series with first term 1,common difference 3 and last term 100

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Q: Does a geometric series always have a finite value?

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Q: Explain why careful analysis is required to determine the convergence or divergence of a series and…

A: Given: convergence and divergence of the series.

Q: What is a geometric series and when does it converge?

A: A geometric series is the sum of the terms in a geometric sequence. The geometric series a + ar +…

Q: Is the series 4k convergent? What is the easiest way to answer this question? Can you tell if 3* xp…

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Q: E converyes 8.) Explain why an= as a Sequence, but 2ñ Series. diverges as a

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Q: (-1)

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Q: 8図 n=1 -1

A: To find the sum and if the series is convergent or divergent.

Q: What are Geometric Series?

A: Geometric series are such finite or infinite series where every next term is obtained by multiplying…

Q: You add a finite number of terms to a convergent series. Will the new series still converge? Explain…

A: According to the question, we have to check the convergent series, what does affect on the series if…

Q: 2.) Write down an example of a series , an such that the terms of the series go to zero, yet the…

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Q: What happens if you add a finite number of terms to a convergent series? A divergent series? What…

A: As there are multiple parts to the question, we will address the par related to divergent series…

Q: Determine whether the series is conivergent or

A: Given ∑n=1∞(-1)n-1nn+2

Q: Explain why the magnitude of the remainder in an alternating series(with terms that are…

A: The magnitude of the remainder in an alternating series (with terms that are nonincreasing in…

Q: If E-ja, is a convergent series of nonnegative numbers, can anything be said about Ea,/n)? Explain.…

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Q: When geometric series does converge, what is its sum?

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Q: can you please answer both questions. Decide whether those two series will converge. Thank you

A: Given series

Q: 5. Determine if each series is coNvergent or divergent, and justify your answers. (-1)" n=2 -

A: We have to show that the given series diverges or converges

Q: 6" 5" – 1 n=1 8.

A: ∑n=1∞6n5n-1

Q: Determine if the series converges or diverges. Give a reason for your answer. 5 - Σ n5"

A: Calculate as following:-

Q: or diverges.

A: Here we have, ∑n=1∞(-1)n+1n+4(n+1)(n+2)=∑n=1∞an ⇒an=(-1)n+1n+4(n+1)(n+2)

Q: Define a geometric series, state when it converges, and give the formula for the sum of a convergent…

A: To Determine: define a geometric series,state when it converges,and give the formula for the sum of…

Q: Determine whether the series is convergent or divergent. If it is convergent, write its sum. Justify…

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Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find the…

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Q: Calculate the sum of the series whose terms are 1, 2, 3, ..., 99.

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Q: The bob of a pendulum swings through an arc 24 centimeters long on its first swing. If each…

A: G.P SeriesA series, in which each term is found by multiplying by the previous term by a fixed term.…

Q: either use the formula for the sum of a geometric series to find the sum or state that the series…

A: Given the sum is 23/7 + 24/72 + 25/73 + 26/74 + ...............∞ This is sum of a ∞ geometric…

Q: What happens if you add a finite number of terms to a divergent series or delete a finite number of…

A: Use the following facts 1) Sum of a finite number of terms is finite 2) If we add or subtract a…

Q: Does the series converge or diverge? Explain.

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Q: Find the sum of the first 10 terms of an arithmetic series defined by: 3, -1, -5 ...

A: Please refer the attached image for complete solution.

Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find the…

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Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find the…

A: First we need to detect the series as divergent or convergent and then find the value if it is…

Q: Explain if the series which is the sum of the terms a sub n = 1/n^(9/4) converge or diverge?

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Q: Please state whether the series converges or diverges

A: We will check whether the given series is convergent or divergent.

Q: Determine whether the series is convegent or divergent. If it is Convergent, find its Sum, 8) nニ2

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Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find the…

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Q: What does it mean for infinite series to diverge?

A: Given: Infinite series to diverge:

Q: i) En=1 100 11

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Q: Determine whether the geometric series is convergent or divergent. If it converges, find its sum. 80…

A: Geometric Series : (3/4)0 + (3/4)1 + (3/4)2 + (3/4)3 + (3/4)4 + ........... 1 + 3/4 + 9/16 + 27/64 +…