The given series is
To apply comparison test we can take the geometric series
So common ration is . This geometric series is convergent as the modulus of the common ratio is less than 1. Also note that
for all large . So by comparison test the given series is convergent. The reason is the terms of the given series is less or equal to the terms of a convergent series. Note that comparison test can be applied to series of positive terms only.
Determine whether 〉· is convergent. Specifically, use the Comparison Test to compare this series...
(1 point) We will determine whether the series n3 + 2n an - is convergent or divergent using the Limit Comparison Test (note that the Comparison Test is difficult to apply in this case). The given series has positive terms, which is a requirement for applying the Limit Comparison Test. First we must find an appropriate series bn for comparison (this series must also have positive terms). The most reasonable choice is ba - (choose something of the form 1/mp...
Use the Ordinary Comparison Test to determine whether the series is convergent or divergent. 7 n - 1 n= 1 3. n = 1 n= 2
n-arctan(n) We want to use comparison test in order to determine whether the series is convergent or divergent. Which of the following is correct? n=2n2n+2n +5 Select one O a. It is divergent by comparison test with the series nen O b. It is convergent by comparison test with the series SIS M8 n c. It is divergent by comparison test with the series n=1nn о d. It is convergent by comparison test with the series 1n2 e. It is...
In your answer state: (a) whether the above series Use the Limit Comparison Test to determine whether the following series is convergent or divergent Σ n +5 3 nin +4 is convergent or divergent, and (b) which series did you compare with the series is divergent, compare with E1 nin the series is convergent, compare with E 1 2. n=in the series is convergent, compare with E 1 nain the series is divergent, compare with 21 nin 1 the series...
7) Use the Ordinary Comparison Test to determine whether the series is convergent or divergent. Υ n (a) (6) Σ η η 5" 3η – 4 M8 M8 (Inn) 2 (c) η (d) tan n2 n3 η-2 1 (e) Σ (6) Σ 2n + 3 2n + 3 ή-1 1-1
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...
(1 pt) Use the Comparison Test to determine whether the infinite series is convergent. 1 Σ. n3" By the Comparison Test, the infinite series n3" T1 A. converges B. diverges Note: You are allowed only one attempt on this problem.
27. [-/1 Points] DETAILS SCALCET8 11.4.019. Determine whether the series converges or diverges. MY NOTES AS 00 + 1 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...
divergent 3. Using comparison test determine whether the following series is convergent or 21/n OC (a) n=1 ( b) Σ n n2-cos2 n ( c) Σ e n =1 n2+cos2 n n 2 =1_2n ( d) Σ ( e) Σ n n n=1 divergent 3. Using comparison test determine whether the following series is convergent or 21/n OC (a) n=1 ( b) Σ n n2-cos2 n ( c) Σ e n =1 n2+cos2 n n 2 =1_2n ( d) Σ...
Use the Limit Comparison Test to determine if the series 2-1 first. na +10 is convergent or diver +n+1