an Q4. If £ an converges and an > 0 for all n , can anything be said about E- ?

Q: If an converges and > 0 for all n , can anything be said about E–? An an

A: Given that, ∑ an  converges We known that, the series if  ∑n = 1∞ an  is convergent then limn→∞ an =…

Q: If lim an 1 then n00 Σ an n=1 converges O diverges O may or may not converge

A:

Q: Which of the following statements is true? O E )" converges to - 2-1 7 12 O E O"' diverges n-1 O E…

A: The geometric series 1+ar+ar2+ar3+....…

Q: Determine whether the given converges or diverges. n Σ 2n + 1 n=1

A: Given is a series ∑n=1∞n2n+1n To check if the given series is convergent or divergent Ratio test:…

Q: Determine whether the following converges or diverges {(5) n 2n +1 n=1

A:

Q: n=1 (ii) Give an example such that a, converges conditionally and diverges. IM:

A: Please see the below picture for detailed solution.

Q: 5. Find all values of x >0 so that ) converges. 3k k=2

A:

Q: What are all of the values of x ,such that Σ (3x)" (-1)"+ 00 converges? n=1

A: To solve this question we shall use root test for series.

Q: (-1)ªn n² + 1 mula converges to a value or diverges withou

A:

Q: 21. Show that E(-1)"+1; 2n converges n! absolutely. n=1

A:

Q: Given: a, = In(n + 1) – In(n) for n E N || Determine if the following is convergent or divergent.…

A: Given  an = lnn+1 - lnn for n∈ℕ.

Q: 00 a is converges, then lim a = 00. n=1

A:

Q: If Σan converges and an > 0 for all n, can anything be said about Σ(1/an)? Give reasons for your…

A:

Q: · E In (e + +) n = 1

A:

Q: If lim a, is not 0 then 2 a, is convergent n=1

A: By using theorem we can say that

Q: 1 79. For which a does converge? n(In n)" n=2

A: Let the given series be - y = ∑n=2∞ 1nlnnuWe can write it as - y = ∫2∞ 1nlnnadn…

Q: 3 - If E is convergent, find its sum. z=1 en n(n+3)

A:

Q: 1 3. En=1 (2n+1)3

A:

Q: Determine whether the given converges or diverges. n 2n +1 n=1

A: We can solve this as follows:

Q: What are all of the values of x ,such that Σ.. (-1)" + 1 converges? (31)"

A:

Q: 5n – 1 8) Σ 7n n=1

A:

Q: If an> 0 and Σ an converges, then Σ(-1)"an converges.

A: We have to check wheather it is true or not

Q: If Ea, converges , then n=1a, diverges n=1 an n=1 Select one: O True O False

A: given sequence are, given that 1st sequence is converges and we have to find 2nd sequence is…

Q: 5. (a) Suppose 1 and Xn+1 = 2 Show that {n} converges and find the limit. X1 for all nEN.

A:

Q: 10. Suppose {an} is a sequence of real numbers and b, the sequence {bn} is convergent, so is {an}. =…

A:

Q: For which values of p does £=1 converge? (1+eon)4p

A: Given: To explain the given statement as follows, .

Q: 34. Assume that an+1/an converges to p = 4. -1 Does > an converge (assume that n=1 An # 0 for all…

A:

Q: (In(n))" 00 Find the value(s) of a such that 2 is convergent T2 Answer:

A: Given that, ∑n=2∞lnnan By using the integral test, ∫2∞lnnandn It can be written as, ∫2∞1nlnnadn

Q: If E an converges, then an/n12 converges. n=1 n=1 O True False

A: True, using Abel's test.

Q: 22n Σ n! n=1

A:

Q: (A) True B) False The sequence {x}to, where xn = Sn² 20" is convergent. n! :

A:

Q: 1 3) For which a does converge? Justify your answer. n(In n)e n=2

A: This question is related to series.

Q: If an and bn both converge, then an bn converges. n=1 n=1 n=1 True False

A:

Q: 25. Let an := n 2 1. Which of these conditions must be met if a, is to converge n+1 to 1? I. for any…

A: Just use definition of convergence.

Q: 1 Use appropriate tests to determine if E(-1)"+1, converges. n* log(n) + n! n=1

A: use appropriate test to determine whether the series ∑n=1∞-1n+11n4logn+n! converges according to…

Q: 5. If En-1 an converges, and if an +1 and a, > 0 for all n, (a) Show that E a converges. (b) Does E1…

A: Since, the sequence is a positive monotonically decreasing sequence, so, is also monotonically…

Q: the following converge or not

A:

Q: If both E Un and E(-un) converges then E Un| n=1 n=1 n=1 is also convergent.

A: It is given that ∑n=1∞un and ∑n=1∞-un converges.

Q: If > an converges, then a converges. n=1 n=1

A:

Q: IV. Determine if the given is convergent or divergent. s In"(n*) 23n2 #4. n=1

A: Given series is ∑n=1∞lnn(n4)23n2

Q: 5. E-1 ne-" n=D1

A:

Q: If E=19, converges conditionally then E,-|a,| diverges Select one: True False

A: If absolut series is divergent than alternate series is convergent.

Q: an converges for some large k, then so will n=1 an- If E n=k

A: We have to check

Q: Suppose that (an) and (bn) are convergent sequences of real numbers with limits an → a and bn → b,…

A:

Q: Determine if the two given converges or diverges. { п n 2n + - 1/ n=1 Σ n n \2n + 1 n=1

A:

Q: O Does Eo 2k+² e-k converge or diverge? If it converges find the sum. "k=1'

A:

Q: Given the expression an = V4n² + 3n – 2n for n >1 Check whether this is convergent or divergent:…

A: solution:-an=4n2+3n-2n   for   n≥1Divergent…

Q: Determine if the given is convergent or divergent. E0, In" (n*) 23n2 n=1

A: