6. Suppose that {an} is a sequence of nonzero real numbers. Suppose that > ak is a convergent series. Explain why 1 must be a k=1 ak k=1 divergent series.

Q: Σ 1 list all the possible tests that can be used to determine the convergence or divergence of this…

A: Given series ∑n=1∞1nen

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

A: The convergent series takes a finite value or we can say that convergent series give a finite sum.

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: 5. Use the Ratio Test to determine whether the series EDai (2n)! converges or diverges. State n=1 if…

A:

Q: How can rearranging the order of terms in an infinite series be different for an absolutely…

A:

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

A:

Q: Determine if the series 2 converges or diverges and state which test can be used to support that…

A: To find whether the series in convergence or divergence

Q: 1 is convergent or divergent. Determine if the series In(3n)

A: Ans is given in following photo added

Q: 5* Find the interval of convergence of the geometric series (x – 4)**

A:

Q: Determine if the series whose nth term is (In 3)" 11 converges or diverges

A:

Q: Find the sum of the convergent series. 3+.

A: We need to evaluate the sum of the following convergent series 3+32+34+38+···········

Q: 5.) Determine the convergence or divergence of the series In n=1

A:

Q: Determine how many terms of the following convergent series must be summed to be sure that the…

A:

Q: Suppose a and b, are series with positive terms and b, is known to be divergent. (a) If a, > b, for…

A: Given: ∑ an  and ∑ bn are series with positive terms and ∑ bn  is known to be divergent. a) If…

Q: What is the remainder of a convergent alternating series whose sum isapproximated by the first N…

A: The remainder of the convergent alternating series is S-Sn. if the alternating series satisfy the…

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

A:

Q: 11. Explain why all the terms of a divergent geometric seriesare nonzero.

A: Solution: We have given geometric series: First of all, we are going to understand the concept of a…

Q: In 2. Determine whether the series E=1 is convergent explain why. 100

A:

Q: Determine if the # isdivergent series or convergent: (-2) )!n n=0

A: Consider a series . If the series is convergent then . If then the series is divergent. This is the…

Q: Determine the convergence or divergence of the series. 2) Σ (-1)" In n=1

A:

Q: 7. Give an example of two series, a, and bn that are divergent, however, (a, + bn) is convergent. WI

A:

Q: Find the sum of the convergent series. Σ n = 0

A: Use sum of formula of infinite term of gp

Q: Suppose a, and b are series with positive terms and b. is known to be convergent. in (a) If a, > b,…

A: Given query is to find select correct option regarding an and bn.

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

A:

Q: Doesthe series * 2n Converge or diverge フー一 30-2

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Q: For what value of r does the infinit Series Sn Convergent

A: Given data÷

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: If the series an , and E (an + b,) are convergent series then b, may be a divergent series. Select…

A:

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: When all the terms in a series are positive, is the sequence of partial sums an increasing sequence…

A:

Q: Suppose a, and b, are series with positive terms and b, is known to be divergent. (a) If a, > b, for…

A: We have two two infinite series with positive terms :∑n=1∞an and ∑n=1∞bn and also we have ∑n=1∞bn is…

Q: , 4" – 3" (a) If the series, ) 5" converges, what is its sum? n=0 in

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If an alternating series is not convergent then it is divergent. Select one: O True O False

A: We can find the answer as below.

Q: 32. Tell if the following infinite series converges or divergesE,)", 8n2

A: Note : “Since you have asked multiple question, we will solve the first question for you. To get…

Q: Suppose we also know that 1> an 0. and a converge. Then the series£ converge Select one: True False

A: By comparison test,

Q: 3 9) Determine whether the series 1- diverges. converges or n=1 8

A:

Q: 3" + 5" mine whether the series 2 6h converges or diverges. If it converges, find its sum. n= 1

A:

Q: Suppose the partial sum sequence of a series is given by SN = N . Then the series converges.

A: Given the partial sum sequence of series is given by SN=1N

Q: 1 Use the root test to determine whether the series 2 4 8. ++ converges or ... diverges. 2 32 54 + +

A: Given the series :

Q: Suppose Fa, and b, are series with positive terms and b, is known to be convergent. (a) If a, > b,…

A: This question is from convergence/divergence.

Q: Find the sum of the convergent series. Σ

A: The given convergent series is, ∑n=0∞-47n To find its sum.

Q: 5. n22

A:

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

A: Find the geometric series which converges to 7.

Q: Use an appropriate test to determine whether the series converges. 9 3 Ink Σ k=3

A: Given ∑k=3∞93ln k  Now,  here use the limit comparison test to determine whether the series…

Q: 2. Determine if the series Σ Σ n=1 πη is absolutely or conditionally convergent.

A:

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: Use an appropriate test to determine whether the series converges. 9 3 Ink M8 Σ k=3 By the this…

A: Comparison test to check the convergence