Determine whether the series converges 8 nn a. sin(n) + cos(n) n3 +n + n +1...
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
(b) Determine whether the series Σ7n+= converges or diverges. n=1 Σ(-1)n+1n2+1 (c) Determine whether the series converges absolutely, con- n= 1 verges conditionally or diverges (d) Find the interval of convergence for the power series Σ(-1)k (2r)* k-2 (b) Determine whether the series Σ7n+= converges or diverges. n=1 Σ(-1)n+1n2+1 (c) Determine whether the series converges absolutely, con- n= 1 verges conditionally or diverges (d) Find the interval of convergence for the power series Σ(-1)k (2r)* k-2
2. Determine whether the series converges in any four (4) of a - f. [20 = 4 x5 each] 27 - 37 ln(n) b. (-3) "e" 47 + (-1) XO a. C. . T=0 โ=0 n=1 18 d. sin(n) + cos(n) ทง + n + n +1 C. (-1) f. " Vn+1 n! 1-0 n=1
0-11 points RogaCalcET3 10.4.027. 8. Determine convergence or divergence by any method. Σ-7 -n3/3 7n n e n=1 The series converges The series diverges. 0-11 points RogaCalcET3 10.4.027. 8. Determine convergence or divergence by any method. Σ-7 -n3/3 7n n e n=1 The series converges The series diverges.
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
Determine whether the following series converges. Justify your answer. 8 + cos 10k Σ k= 1 Select the correct answer below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) 8+ cos 10k 9 O A. Because 9 E and, for any positive integer k, E converges, the given series converges by the Comparison Test. 8 k=1 00 OB. The Integral Test yields f(x) dx = so the series diverges by the Integral...
Determine whether the series converges or diverges. n + 1 Σ +n n = 1 The series converges by the Limit Comparison Test. Each term is less than that of a convergent geometric series. The series converges by the Limit Comparison Test. The limit of the ratio of its terms and a convergent p-series is greater than 0. The series diverges by the Limit Comparison Test. The limit of the ratio of its terms and a divergent p-series is greater...
Use the alternating series test to determine whether the series converges or diverges. Do 1 problem. 2n 1) Σ-1)". 2) Σ-1)" 3) Σ-1)**1. 4) 4η + 3 8 + 1η 4n' +2 cos(ηπ) 1 5) Στο Hel
13. Find the sum of each series. a. En=1(tan-In- tan-(n + 1)) 6. Σ=1 nn+2) 14. Determine whether each series converges absolutely, converges conditionally, or diverges. Be sure to show your reasoning and state any test(s) used. b. Σ=1; Page 18 of 18 C. Σ. 2(tan-n)" δ. Σο1 242 Σα (-1)+1η
Use the pull down menu to state whether the series converges or diverges and by which convergence test. 3m 4 (1y Vn+3 8" n! g0- 32 443 (-1'n Σ 4n+4 00 Σ (+: 4 4 n7 n15 W Converges-Integral/Comparison Test Converges-Ratio Test Converges-Alternating Series Test Diverges-Integral/Comparison Test Diverges-Ratio Test Diverges-Alternating Series Test Use the pull down menu to state whether the series converges or diverges and by which convergence test. 3m 4 (1y Vn+3 8" n! g0- 32 443 (-1'n...