The series ∑1/n2+2n+1 is convergent by the Ratio Test.
TRUE
FALSE
Part A [15 Points]: Choose TRUE or FALSE for each of the following items. 1. If the series anx" converges, then anx" → as n 700. TRUE FALSE 2. The series & {-1}" is absolutely convergent. TRUE FALSE 3. The series 2 is convergent using the Ratio Test. TRUE FALSE 00 4. The series An- n n2+1 is convergent using the Geometric Series Test. TRUE FALSE 5. The series 2n=1 42+2n+3 (-1)" is conditionally convergent. TRUE FALSE
(a) (1 point) Determine whether the following series is convergent or divergent. (2n)! (b) (1 point) Find the sum of the following series ΣIn ( na + 2n +1 n2 + 2n n=1
please give all steps Determine, using the ratio test, whether the following series is convergent or divergent 3" (-1)" 2n(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...
Determine whether 〉· is convergent. Specifically, use the Comparison Test to compare this series to a geometric series. Claim: is convergent (please answer true or false) The common ratio of the geometric series suitable for applying the Comparison Test isr- Claim: bn = 22n+7. 2+7. and an satisfy (1) 0 3 an n for all large n 2 1 or (2)0 Sbn al large n 2 1) (please enter (1) or (2). Determine whether 〉· is convergent. Specifically, use the...
Use the Integral Test to determine whether the series is convergent or divergent. ∞ n n2 + 8 n = 1 Evaluate the following integral. ∞ 1 x x2 + 8 dx Since the integral finite, the series is . Use the Integral Test to determine whether the series is convergent or divergent. n2 8 Evaluate the following integral. OO dx Since the integral ---Select--- finite, the series is ---Select---
(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 Ratio Test to determine whether the series is convergent or divergent. Use the Ratio Test to determine whether the series is convergent or divergent. Identify an (-3)" Evaluate the following limit. Since im. 1972 12V1--Select-
(1 point) Select the FIRST correct reason why the given series converges. A. Convergent geometric series B. Convergent p series C. Comparison (or Limit Comparison) with a geometric or p series D. Alternating Series Test E. None of the above 1. n² + √n n4 – 4 sin?(2n) n2 E 4 (n + 1)(9)" n=1 2n + 2 cos(NT) 16. In(3n)
Use the Integral Test to determine whether the series is convergent or divergent. ∞ n n2 + 2 n = 1 Evaluate the following integral. ∞ 1 x x2 + 2 dx