2. When can you say that a SERIES or SEQUENCE diverges? Prove it using mathematical approach.

Q: n = 0

A:

Q: Determine whether the following statement is true or false, and explain why.

A: The given statement: An infinite geometric series converges as long as -1≤r≤1.

Q: What is the sum of the series corresponding to sequence: 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9,…

A: We have to find sum of the series:

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: Give an example of a divergent infinite series whose general term tends to zero.

A:

Q: 9. find the of the geometric series. sum if possible. 3(2)"-! nil

A: We have to find sum

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: Determine the convergence or divergence of the series. (If you need to use

A: answer is in next step

Q: What are the radius and interval of convergence of the geometric series ∑xk?

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Q: Write the first four terms of the infinite geometric series with first term a = 5 and common ratio r…

A:

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: What is the condition for convergence of the geometric series Zark?

A:

Q: 8. Write an argument to determine whether the series > converges or diverges. If it is k=1…

A: The objective is to write an argument to determine whether the series convergence or divergence.

Q: Using the first five terms of a sequence formed by (3n - 2), what series will be formed?

A:

Q: Σ, 6 what is the value of the series

A: Sum of the infinite terms of geometric series whose first term is  'a' and common ratio is 'r' is…

Q: Find the Generating function for the sequence 1,3,9,27,81,. Also find for which value the series…

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Q: Σ 6" 7" Find the sum of the convergent series

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Q: Apply the Ratio Test to show whether the infinite series is convergent or divergent n! Σ (-2)"

A: Given problem:-

Q: 1 converge? What are the values of x that would make the series

A:

Q: Does rearranging the terms of a convergent series change the sum of the series? Explain.

A: According to the question, we have to explain whether rearranging the terms of a convergent series…

Q: Discuss the similarities and differences between what it means for a sequence to converge and what…

A: Let's find.

Q: Explain why you think the series E (E) converges to a finite 1-(-1)" n+1 number or diverges. If the…

A:

Q: Discuss all the cases of the Infinite Geometric Series.

A: To discuss about the cases of infinite geometric series

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

A:

Q: Determine whether the geometric series is convergent or divergent. 25 (3 – 5 + 125 + 9. ··) ..

A:

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: Converges (by geometric series)

A: If  the geometric series is given by: ∑n=0∞arn=a+ar+ar2+..... If r<1 then geometric series…

Q: Determine whether the statement, 'The sum of the geometric series 1/2 + 1/4 + 1/8 + ..... + 1/512…

A: Given: Geometric series is 12+14+18+⋯⋯+1512 Here, first term is a=12 Common ratio, r=1412=12 We know…

Q: 2) Explain, in your own words, what it means for an infinite series to converge.

A: We have to explain the meaning of convergene of a infinite series.

Q: 5. Apply methods discussed to determine if the series converges or your conclusion. diverges.…

A:

Q: Make up a geometric series Σarn-1 that converges to the number5 if a = 13/2.

A: Given:

Q: Evaluate the geometric series and compute the sum if convergent. 5 −5+ _5+3/2 4 - +

A: Solution

Q: How can you estimate the error involved in approximating the sum of an alternating series with one…

A: The alternating series test:

Q: use the Direct Comparison Test to determine whether the infinite series is convergent.

A:

Q: Astudent argues that (-1)" /n is an alternating series and therefore converges. Is the student…

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Q: Under what circumstances will an infinite series of nonnegative terms converge? Diverge? Why study…

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Q: How would you classify the sequence 0.45,0.045, 0.0045, 0.00045, ........... А. Arithmetic Series В.…

A: 0.45, 0.045, 0.0045, 0.00045,..........a1=0.45a2=0.045a3=0.0045a4=0.00045Ratios of two adjacent…

Q: What is the formula for the nth partial sum of the series? If the series is convergent, what is the…

A:

Q: (c) Express the number 1.234567 as a fraction (in its simplest form) using the sum of a geometric…

A: Ans=45679/37000 For detail...go through the solution.....I have solved step by step in detail

Q: D) what is the upper bound for your error estimate if you use the first 12 terms (use the…

A: Given, To evaluate upper bound for your error estimate if you use the first 12 terms (use the…

Q: 4) Find a geometric series that converges to 7.

A: Find the geometric series which converges to 7.

Q: What is the sum of a convergent geometric series?

A: A geometric series is a series whose related sequence is geometric. The sum of an infinite number of…

Q: 2.) Determine whether the geometric series is convergent or divergent. If it is Σ(13) " n=1…

A: To determine  whether the given geometric series is convergent or divergent. If it is convergent, to…

Q: What is the sum of the infinite series "n =1 102" ? Show your work

A:

Q: しイ is it converyes k=) 3k and diverges what's the Sum of series ?

A:

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

A: Given: Infinite series to diverge: