# Pt use the integral test to determine whether the

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5. (1 pt) Use the Integral Test to determine whether the infinite series is convergent. You are allowed only one attempt on this problem. Fill in the corresponding integrand and the value of the improper integral. 2 . Note: You are allowed only one attempt on this problem. n 2 .
Enter inf for , -inf for - , and DNE if the limit does not exist. n = 1 R n = 1
Compare with 2 dx = By the Integral Test, the infinite series n = 2 10 ne - n 2 A. converges B. diverges By the Comparison Test we can therefore conclude that series n = 1 sin 4 n n 2 also converges. Answer(s) submitted: A (correct) Note: You are allowed only one attempt on this problem.
Answer(s) submitted: 10*x*eˆ(-xˆ2) 0-(-5*eˆ(-4)) A (correct) Correct Answers: 10*x*eˆ(-xˆ2) 0.0915782 A 6. (1 pt) Use the Comparison Test to determine whether the infinite series is convergent. n = 1 sin 4 n n 2 By the Comparison Test, the infinite series n = 1 sin 4 n n 2 A. converges B. diverges Solution: We compare with the geometric series 1 3 n . For n 1, 1 n 3 n 1 3 n = 1 3 n . Since n = 1 1 3 n converges (it’s a geometric series with | r | = 1 3 < 1 ), we conclude by the Comparison Test that n = 1 1 n 3 n also converges. Answer(s) submitted: A (correct) Correct Answers: A 2
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