Homework Answers
a) Use the special series and convergence test table to find the sum of the series....
a) Use the special series and convergence test table to find the sum of the series. Be sure to show all work and substitutions. 00 3 8n NO For parts b, c, d, and e, show that the series converges or diverges. The table of special series and convergence tests should be used. Identify the type of convergence test used and be sure to show all work. (Hint: two should diverge) b) 2 + 7 con Σ Test: (-1) in...
3. A sequence is a map a N°R, typically written (an) = (ao, a1, a2, a3, a4,) As an example, the sequence (an) = 1/(...
3. A sequence is a map a N°R, typically written (an) = (ao, a1, a2, a3, a4,) As an example, the sequence (an) = 1/(n2 +1) begins (1, 1/2, 1/5, 1/10, 1/17,..) Here is a useful fact relating sequences and continuity: A function f(x) is continuous at x c if and only if for every sequence (an) that converges to c, written anc, then f(x,) f(c). Alternatively, if you and f(yn)L" with L' L", then f is not continuous at...
6. (25 points) Determine all positive values of p for which the series Lin=2 n(log2 n)...
6. (25 points) Determine all positive values of p for which the series Lin=2 n(log2 n) 2. (15 points) Determine whether the sequence { v3.3.FI converges or not. If it n=1 converges, find the limit. If it diverges, specify whether it diverges to 00, -00, or neither. Is the sequence bounded? Explain. 4n+1 3. (15 points) Determine whether the series Emai gn=1 converges or not. If it converges, find the sum. 4. (10 points) Write 0.1257 as a fraction. 5.(20...
f. 20 2. Determine whether the series converges in any four (4) of a 2 -...
f. 20 2. Determine whether the series converges in any four (4) of a 2 - 3 b. (-3)="" 4r + (-1)" 4x5 each) In(n) 00 a. c. n n0 n=1 M8 iM d. Σ sin(n) + cos(n) n3+ n2 +n +1 e. f. Σ n! (-1)" Vn+1 n=0 n2
12. Determine whether the following series converge or diverge. (a) (b) 2-nzn-1 4n n=0 n=1 4n...
12. Determine whether the following series converge or diverge. (a) (b) 2-nzn-1 4n n=0 n=1 4n (-1)n+1 loge n (c) (d) 7n + 1 n n=1 n=3 iM: M: Mį M8 sinn (e) ✓n n2 + 2 (f) n2 n=1 n=1 2n en (g) (h) Vn! n=1 n=1
005 10.0 points Determine whether the sequence {an} con- verges or diverges when en = (-1)"...
005 10.0 points Determine whether the sequence {an} con- verges or diverges when en = (-1)" (5n+) (5n+7) (5n+4) and if it does, find its limit. 1. sequence diverges 2. limit = 0 3. limit = +1 4. limit 5. limit = 1 006 10.0 points Which of the following sequences converge? A. _2n | 3n +4J 4en +6) 5n+6 C. {_3en1 C. (4+2en) 1. A and C only 2. B only 3. none of them 4. A, B, and...
All of question 2 please 1. True or false: (15 pts) {(-1)" tan (TC/2-3/n} is oscillating....
All of question 2 please
1. True or false: (15 pts) {(-1)" tan (TC/2-3/n} is oscillating. (b) 1/2-1/4+1/6-1/8+1/10-..... converges conditionally. A convergent sequence is always Cauchy. {1/n) is a Cauchy sequence. (1-3)-(1-31/2)+(1-313)-(1-314 )+.....diverges. 2. Find limit sup and limit inf of the following sequences: (10 pts) (a){c+4) sin ng (b) {(1+m+)"} Limsup= limsup= Lmitinf= liminf= 3. Prove that either the following sequence has a limit or not. (20 pts) (a) 2n (b) n2+4n+2 n+6vn n-1
Question 1 please 1. True or false: (15 pts) {(-1)" tan (TC/2-3/n} is oscillating. (b) 1/2-1/4+1/6-1/8+1/10-........
Question 1 please
1. True or false: (15 pts) {(-1)" tan (TC/2-3/n} is oscillating. (b) 1/2-1/4+1/6-1/8+1/10-..... converges conditionally. A convergent sequence is always Cauchy. {1/n) is a Cauchy sequence. (1-3)-(1-31/2)+(1-313)-(1-314 )+.....diverges. 2. Find limit sup and limit inf of the following sequences: (10 pts) (a){c+4) sin ng (b) {(1+m+)"} Limsup= limsup= Lmitinf= liminf= 3. Prove that either the following sequence has a limit or not. (20 pts) (a) 2n (b) n2+4n+2 n+6vn n-1
(-1)-1 n2 is absolutely convergent. 1. (2 points) Prove that cos n is convergent or divergent....
(-1)-1 n2 is absolutely convergent. 1. (2 points) Prove that cos n is convergent or divergent. 2. (2 points) Determine whether the series - (Use cos n<1 for all n) 3. (3 points) Test the series -1) 3 for absolute convergence. (Use the Ratio Test) 2n +3) 4. (3 points) Determine whether the series converges or diverges. 3n +2 n-1 (Use the Root Test) 5. (3 points) Find R and I of the series (z-3) 1 Find a power series...
#3 n-1 Determine whether the series 2 35 n=1 converges or diverges. If it converges, find...
#3 n-1 Determine whether the series 2 35 n=1 converges or diverges. If it converges, find its sum. #41 00 n-1 Analyze for convergence (6) NO -0") . Find the sum in case the series converges. n=1
a) Use the special series and convergence test table to find the sum of the series. Be sure to show all work and substitutions. 00 3 8n NO For parts b, c, d, and e, show that the series converges or diverges. The table of special series and convergence tests should be used. Identify the type of convergence test used and be sure to show all work. (Hint: two should diverge) b) 2 + 7 con Σ Test: (-1) in...
3. A sequence is a map a N°R, typically written (an) = (ao, a1, a2, a3, a4,) As an example, the sequence (an) = 1/(n2 +1) begins (1, 1/2, 1/5, 1/10, 1/17,..) Here is a useful fact relating sequences and continuity: A function f(x) is continuous at x c if and only if for every sequence (an) that converges to c, written anc, then f(x,) f(c). Alternatively, if you and f(yn)L" with L' L", then f is not continuous at...
6. (25 points) Determine all positive values of p for which the series Lin=2 n(log2 n) 2. (15 points) Determine whether the sequence { v3.3.FI converges or not. If it n=1 converges, find the limit. If it diverges, specify whether it diverges to 00, -00, or neither. Is the sequence bounded? Explain. 4n+1 3. (15 points) Determine whether the series Emai gn=1 converges or not. If it converges, find the sum. 4. (10 points) Write 0.1257 as a fraction. 5.(20...
f. 20 2. Determine whether the series converges in any four (4) of a 2 - 3 b. (-3)="" 4r + (-1)" 4x5 each) In(n) 00 a. c. n n0 n=1 M8 iM d. Σ sin(n) + cos(n) n3+ n2 +n +1 e. f. Σ n! (-1)" Vn+1 n=0 n2
12. Determine whether the following series converge or diverge. (a) (b) 2-nzn-1 4n n=0 n=1 4n (-1)n+1 loge n (c) (d) 7n + 1 n n=1 n=3 iM: M: Mį M8 sinn (e) ✓n n2 + 2 (f) n2 n=1 n=1 2n en (g) (h) Vn! n=1 n=1
005 10.0 points Determine whether the sequence {an} con- verges or diverges when en = (-1)" (5n+) (5n+7) (5n+4) and if it does, find its limit. 1. sequence diverges 2. limit = 0 3. limit = +1 4. limit 5. limit = 1 006 10.0 points Which of the following sequences converge? A. _2n | 3n +4J 4en +6) 5n+6 C. {_3en1 C. (4+2en) 1. A and C only 2. B only 3. none of them 4. A, B, and...
All of question 2 please
1. True or false: (15 pts) {(-1)" tan (TC/2-3/n} is oscillating. (b) 1/2-1/4+1/6-1/8+1/10-..... converges conditionally. A convergent sequence is always Cauchy. {1/n) is a Cauchy sequence. (1-3)-(1-31/2)+(1-313)-(1-314 )+.....diverges. 2. Find limit sup and limit inf of the following sequences: (10 pts) (a){c+4) sin ng (b) {(1+m+)"} Limsup= limsup= Lmitinf= liminf= 3. Prove that either the following sequence has a limit or not. (20 pts) (a) 2n (b) n2+4n+2 n+6vn n-1
Question 1 please
1. True or false: (15 pts) {(-1)" tan (TC/2-3/n} is oscillating. (b) 1/2-1/4+1/6-1/8+1/10-..... converges conditionally. A convergent sequence is always Cauchy. {1/n) is a Cauchy sequence. (1-3)-(1-31/2)+(1-313)-(1-314 )+.....diverges. 2. Find limit sup and limit inf of the following sequences: (10 pts) (a){c+4) sin ng (b) {(1+m+)"} Limsup= limsup= Lmitinf= liminf= 3. Prove that either the following sequence has a limit or not. (20 pts) (a) 2n (b) n2+4n+2 n+6vn n-1
(-1)-1 n2 is absolutely convergent. 1. (2 points) Prove that cos n is convergent or divergent. 2. (2 points) Determine whether the series - (Use cos n<1 for all n) 3. (3 points) Test the series -1) 3 for absolute convergence. (Use the Ratio Test) 2n +3) 4. (3 points) Determine whether the series converges or diverges. 3n +2 n-1 (Use the Root Test) 5. (3 points) Find R and I of the series (z-3) 1 Find a power series...
#3 n-1 Determine whether the series 2 35 n=1 converges or diverges. If it converges, find its sum. #41 00 n-1 Analyze for convergence (6) NO -0") . Find the sum in case the series converges. n=1
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