Below the false statements, explain why they are false. 1. If the limit of {an} is non-zero, it's guaranteed that the series a, diverges. 2. If the limit of {Sn} is five, it's guaranteed that the sequence {an} diverges. 3. If the limit of {an} is zero, it's guaranteed that the series E an converges.

Q: Use the Root Test to determine whether the series convergent or divergent. 3n -5n n + 1 n = 2…

A:

Q: Each of the following statements is an attempt to show that a given series is convergent or…

A: Since you have asked multiple questions, we will solve the first three questions for you. If you…

Q: Each of the following statements is an attempt to show that a given series is convergent or…

A:

Q: For item 2, show that the series satisfies the conditions for the indicated test of convergence…

A: Find the integration of the given function over the range  of 8 to  inf

Q: By 6/2silon definition, check the Convergenre of the following Sequenies. = 2n21

A: Given that, Sn=2n2+12n2-1 We find the limit of this sequence as follows:…

Q: 1.2 1.2.3, 1.2.3.4 + ... 1.3 1.3.5 1.3.5.7

A:

Q: Use the Ratio Test to determine whether the series convergent or divergent. n! "ח n = 1 Identify an…

A:

Q: Suppose that (a) n=0 Cnxn converges when x = -4 and diverges when x = 6. What can be said about the…

A: As per company guidelines we are allowed to solve maximum three sub-parts so i am solving first…

Q: You will use the Ratio Test to determine whether the series is convergent or divergent. First, Copy…

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: For each of the folowing series, determine whether it is convergent or divergent. Justify your…

A: We have to check the given is convergent or divergent.

Q: Use the Ratio Test to determine whether the series is convergent or divergent. n=1 (n + 1)82n +1…

A: The given series is, Compare the series, To find an+1, replace n by n + 1 in the equation for an,…

Q: 1a. The limit of the nth term of a series converges to 0. What can you conclude about the…

A:

Q: Determine the convergence state and limit of the sequence with the general term an=(1−(9/n2))7n,…

A:

Q: Find the sum of the convergent series. 00 4 п(п + 2) n=1

A: Given series,

Q: Use the Ratio Test to determine whether the series convergent or divergent. n! n = 1 Identify an…

A:

Q: 2 should be used to estimate its value with error at most 0.000001? How many terms of the convergent…

A: Here one convergent series is given and estimate the terms of the convergent series of its value…

Q: Use series to evaluate the limits

A: Given: limx→0ex-e-xx we know that…

Q: Use the Ratio Test to determine whether the series convergent or divergent. Σ n=1 Identify an…

A: Given the series ∑n=1∞n!nn. The objective is to show that the series is convergent or divergent…

Q: opose that Cex" converges when x = -4 and diverges when x= 6. What can be said about the convergence…

A: The given statement implies that the series is convergent for |x|<4 And divergent for |x|>4 We…

Q: Is the series Σ (3j)"n! n" n=1 convergent or divergent? Give a reason for your answer and show the…

A:

Q: The series C,(x +3)" converges at æ = 2 and diverges at æ = -12. Based on this information, what can…

A:

Q: Each of the following statements is an attempt to show that a given series is convergent or…

A:

Q: 2. . For each of the following SEQUENCES, determ converges, find the limit. (GIVE REASONS FOR for…

A: a.   an=1+0.7nb.   an=nlnn n=2,3,4,...

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

A:

Q: Use the Root Test to determine whether the series convergent or divergent. ∞ n² + 1 n 4n² + 5. n = 1…

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: (-1)r+1 Vn + 1 n+ 1 10. -1)n+1, N=1

A:

Q: Explain why you think the series n=1 converges to a finite number n+1 or diverges. If the series…

A:

Q: Give an example of two convergent series E1 *k and E1 Yk such that = *kYk diverges. Can this happen…

A:

Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-8)" n? n = 1…

A:

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: Use the Ratio Test to determine whether the series is convergent or divergent. (-9)" n2 n = 1…

A:

Q: Find the values of the convergent series   [From n=3 to infinity] E(-1/3)^3n *that E is the sum…

A: The series can be expressed as follows.

Q: Determine if the series converges. If it converges find the limit. (In n)2 an

A: Series integral test:   The series ∑nan is converges if the integral ∫n f(n) dn converges and…

Q: Use the Ratio Test to determine whether the series is convergent or divergent. n! 104" n = 1…

A: The series is given by ∑n=1∞n!104n To determine : The convergence of the series using Ratio Test.

Q: Use the Root Test to determine whether the series convergent or divergent. Σ n2 + 4 6n2 + 7 n = 1…

A:

Q: I am having trouble understanding this series and its similar sequences. Considering the series in…

A:

Q: hat is the limit as n goes to infinity of the power series (log n)2/nxn ?

A:

Q: The series from n=1 to infinity of n(n+4)/sqrt(n^3+5n^2.  Does it converge or diverge?

A: Take n2  common from the denominator and then go ahead

Q: Suppose a, and b, are series with only positive terms and b, is known to be n=1 n= 1 n = 1…

A: Solve the following

Q: If Ea, is a convergent series of positive terms, prove that Esin (a„) converges.

A:

Q: Use the Ratio Test to determine whether the series is convergent or divergent. n = 1 Identify an-…

A:

Q: For the series determine whether it converges or whether it diverges. As part of your solution,…

A: Given series ∑k=0∞1k3

Q: Pennstase 2) 2Determine whether the given sequence converges or n2+ 1 ldiverges. If it converges,…

A: The objective is to determine whether the given sequence converges or diverges .

Q: Each of the following statements is an attempt to show that a given series is convergent or…

A:

Q: Suppose that Cnxn converges when x = -4 and diverges when x = 6. What can be said about the…

A: The posted question has multi parts. But according to guidelines we will solve the first three…

Q: 4. If > Cn (T + 2)" converges for -5 < x < 1, find the radius of convergence of the series. n=1

A: The given power series is cn(x+2)n , n from 1 to infinity.

Q: Consider the series E, an where an = (-1)"(mM) yn In this problem you must attempt to use the Root…

A:

Q: The three series E An, E Bn, and E C, have terms n8 Сп Bn п An n4

A:

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.