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1. A series Can has the property that lim on = 0. Which of the following...
1. A series has the property that lim an = 0. Which of the following is...
1. A series has the property that lim an = 0. Which of the following is true? (a) The series converges and has the sum 0. (b) The series is convergent but its sum is not necessarily 0. (c) The series is divergent. (a) There is not enough information to determine whether the series converges or diverges. 1 n-00 2 2. A sequence {sn} of partial sums of the series an has the property that lim sn Which of the...
n+00 1. A series an has the property that lim an = 0. Which of the...
n+00 1. A series an has the property that lim an = 0. Which of the following is true? n=1 (a) The series converges and has the sum 0. (b) The series is convergent but its sum is not necessarily 0. (c) The series is divergent. (d) There is not enough information to determine whether the series converges or diverges.
1 n+00 2 n=1 A sequence {$n} of partial sums of the series an has the...
1 n+00 2 n=1 A sequence {$n} of partial sums of the series an has the property that lim Sn = Which of the following is true? 1 (a) lim an = 0. (b) lim an (c) lim an does not exist. (d) There is no way to determine the value of lim an. n+00 noo n+00 n+00 1 n The sequence {en} of partial sums of the series an has the property that sn = n=1 for every positive...
Please answer all parts. (1 point) Series: A Series (Or Infinite Series) is obtained from a sequence by adding the term...
Please answer all parts.
(1 point) Series: A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence. Another sequence associated with the series is the sequence of partial sums. A series converges if its sequence of partial sums converges. The sum of the series is the limit of the sequence of partial sums For example, consider the geometric series defined by the sequence Then the n-th partial sum Sn is given by tl...
12-1 + + 4. The series £9) .. is a geometric series. 4 n=1 Which of...
12-1 + + 4. The series £9) .. is a geometric series. 4 n=1 Which of the following is true? (a) The series is convergent and its sum is less than 1/2. (b) The series is convergent and its sum is 1/2. (c) The series is convergent and its sum is 2/3. (d) The series is convergent and its sum is more than 2/3. IS 5. For positive numbers a and r, it is known that the geometric series divergent....
6. True or False. If the statement is true, explain why using theorems/tests from class, and...
6. True or False. If the statement is true, explain why using theorems/tests from class, and if the statement is false provide a counter example. (a) If an and are series with positive terms such that is divergent and an <by for all r, then an is divergent. I (b) If a, and be are series with positive terms such that is convergent and an <br for all 17, then an is convergent. (e) If lim 0+1 = 1 then...
6. We want to use the Integral Test to show that the positive series a converges....
6. We want to use the Integral Test to show that the positive series a converges. All of the following need to be done except one. Which is the one we don't need to do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = a, for all n. (b) Show that ſ f(z) dr converges. (e) Show that lim Ss6 f(x) dx exists. (d) Show that lim sexists. 7. Suppose...
(Exercise 4.13, reordered) Given a series ΣΧί ak, let 8,-Ση-i ak. Σχί ak is Cesaro summable if S1 + 82 +... +Sn lim n-+...
(Exercise 4.13, reordered) Given a series ΣΧί ak, let 8,-Ση-i ak. Σχί ak is Cesaro summable if S1 + 82 +... +Sn lim n-+o converges. (a) Give an example of a series Σ00i ak that is Cesaro sum mable but not convergent (b) Prove that if 1 ak converges, then it is Cèsaro summable. Hint: Say the sequence of partial sums sn → L. Try to prove that =1 8k → L by showing and then splitting the latter sum...
Step Now we can see that b-14b - 14b 1e-14 196 1 15 -1 lim 0-...
Step Now we can see that b-14b - 14b 1e-14 196 1 15 -1 lim 0- 14- 196 14 Submit Skip (you cannot come back) Step 2 13 is continuous, positive, and decreasing on [1, o), we consider the since f(x)= For al3 13 n= 1 following. (If the quantity diverges, enter DIVERGES.) 13 13 13 13 dx=lim - 12(b)12 12(112 x13 12 b Submit Skip (you cannot come back) Determine whether the series is convergent or divergent. 4n+15-n n=...
n-1 1 1 1 4. The series $0 = 1 + +... is a geometric series....
n-1 1 1 1 4. The series $0 = 1 + +... is a geometric series. 2 2 4 8 n=1 Which of the following is true? (a) The series is convergent and its sum is less than 1/2. (b) The series is convergent and its sum is 1/2. (c) The series is convergent and its sum is 2/3. (d) The series is convergent and its sum is more than 2/3.
1. A series has the property that lim an = 0. Which of the following is true? (a) The series converges and has the sum 0. (b) The series is convergent but its sum is not necessarily 0. (c) The series is divergent. (a) There is not enough information to determine whether the series converges or diverges. 1 n-00 2 2. A sequence {sn} of partial sums of the series an has the property that lim sn Which of the...
n+00 1. A series an has the property that lim an = 0. Which of the following is true? n=1 (a) The series converges and has the sum 0. (b) The series is convergent but its sum is not necessarily 0. (c) The series is divergent. (d) There is not enough information to determine whether the series converges or diverges.
1 n+00 2 n=1 A sequence {$n} of partial sums of the series an has the property that lim Sn = Which of the following is true? 1 (a) lim an = 0. (b) lim an (c) lim an does not exist. (d) There is no way to determine the value of lim an. n+00 noo n+00 n+00 1 n The sequence {en} of partial sums of the series an has the property that sn = n=1 for every positive...
Please answer all parts.
(1 point) Series: A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence. Another sequence associated with the series is the sequence of partial sums. A series converges if its sequence of partial sums converges. The sum of the series is the limit of the sequence of partial sums For example, consider the geometric series defined by the sequence Then the n-th partial sum Sn is given by tl...
12-1 + + 4. The series £9) .. is a geometric series. 4 n=1 Which of the following is true? (a) The series is convergent and its sum is less than 1/2. (b) The series is convergent and its sum is 1/2. (c) The series is convergent and its sum is 2/3. (d) The series is convergent and its sum is more than 2/3. IS 5. For positive numbers a and r, it is known that the geometric series divergent....
6. True or False. If the statement is true, explain why using theorems/tests from class, and if the statement is false provide a counter example. (a) If an and are series with positive terms such that is divergent and an <by for all r, then an is divergent. I (b) If a, and be are series with positive terms such that is convergent and an <br for all 17, then an is convergent. (e) If lim 0+1 = 1 then...
6. We want to use the Integral Test to show that the positive series a converges. All of the following need to be done except one. Which is the one we don't need to do? (a) Find a function f(x) defined on [1,00) such that f(x) > 0, f(x) is decreasing, and f(n) = a, for all n. (b) Show that ſ f(z) dr converges. (e) Show that lim Ss6 f(x) dx exists. (d) Show that lim sexists. 7. Suppose...
(Exercise 4.13, reordered) Given a series ΣΧί ak, let 8,-Ση-i ak. Σχί ak is Cesaro summable if S1 + 82 +... +Sn lim n-+o converges. (a) Give an example of a series Σ00i ak that is Cesaro sum mable but not convergent (b) Prove that if 1 ak converges, then it is Cèsaro summable. Hint: Say the sequence of partial sums sn → L. Try to prove that =1 8k → L by showing and then splitting the latter sum...
Step Now we can see that b-14b - 14b 1e-14 196 1 15 -1 lim 0- 14- 196 14 Submit Skip (you cannot come back) Step 2 13 is continuous, positive, and decreasing on [1, o), we consider the since f(x)= For al3 13 n= 1 following. (If the quantity diverges, enter DIVERGES.) 13 13 13 13 dx=lim - 12(b)12 12(112 x13 12 b Submit Skip (you cannot come back) Determine whether the series is convergent or divergent. 4n+15-n n=...
n-1 1 1 1 4. The series $0 = 1 + +... is a geometric series. 2 2 4 8 n=1 Which of the following is true? (a) The series is convergent and its sum is less than 1/2. (b) The series is convergent and its sum is 1/2. (c) The series is convergent and its sum is 2/3. (d) The series is convergent and its sum is more than 2/3.
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