For the series <1-1n in n +1 n=1 1. Does it converge? 2. Does it absolutely...
For what values of x does the series converge absolutely? S (-1)" (2 +9) -1 -10 4 % < -8 -10 E 48 -10 4 0 4 -8 -10 4 8
Does the series converge or dliverge? 1. nel n Does the series converge absolutely, converge conditio 2. n-2 vn-1 3nn! 3. Does the series converge or diverge? 2-6.10.(4n+ 2) Does the series converge or diverge? 4. 2 nln n
Does the series converge or dliverge? 1. nel n Does the series converge absolutely, converge conditio 2. n-2 vn-1 3nn! 3. Does the series converge or diverge? 2-6.10.(4n+ 2) Does the series converge or diverge? 4. 2 nln n
Does the series converge absolutely or conditionally, or
diverge? Please show appropriate tests.
> (-1)^+1 en + 3 N=1
Prove the ratio test . What does this tell you if
exists?
(Ratio test) If
for all sufficiently large n and some
r < 1, then
converges absolutely; while if
for
all sufficiently large n, then
diverges.
lim |.1n+1/01 700 In+1/xn < We were unable to transcribe this image2x+1/2 > 1 We were unable to transcribe this image
a < 1. Show the series on -a, a] to onverges uniformly 25.9 (a) Let 0 (b) Does the series Explain converge uniformly on (-1,1) to =0
Suppose q is a constant and q> 4. 2"(n + 1)! (a) (5 marks) Does the sequence {an}, where an = – -, converge or diverge? Justify your answer. 2(n+1)! (b) (6 marks) Does the series - converge or diverge? Justify your answer and state the name(s) of any test(s) you used.
Does the series (-1)" (n + 2)" ? converge absolutely, converge conditionally, or diverge? (5n)" Choose the correct answer below and, if necessary, fill in the answer box to complete your choice O A. The series converges absolutely because the limit used in the Root Test is OB. The series diverges because the limit used in the nth-Term Test is different from zero, OC. The series converges conditionally per the Alternating Series Test and because the limit used in the...
please show all steps
00 Does the series 2 (-1)n +16+n 8+n converge absolutely, converge conditionally, or diverge? n=1 Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. O A The series diverges because the limit used in the Ratio Test is not less than or equal to 1. OB. The series converges absolutely because the corresponding series of absolute values is geometric with Ir] =- Oc. The series converges conditionally per...
Exercise 3. Suppose that |2 < 2. Prove that the series converges absolutely.
Exercise 1.20. Show that the series 7t 12 +22m-52 32z-10m2 converges absolutely for |2l< 1