Each of the following statements is an attempt to show that a given series is co

Question

Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. For all n > 1, In(n)/n^2 1, 1/n In(n) 2, In(n)/n > 1/n, and the series sigma 1/n diverges, so by the Comparison Test, the series sigma In(n)/n diverges. For all n > 1, arctan(n)/n^3 2, n^3/n^3 - 2 2, 1/n^2 - 3

Explanation / Answer

(1)

Correct :

because 1/(n^(1.5)) is convergent

(2)

Correct:

Because 1/n diverges

(3)

Correct

because 1/n diverges

(4)

Correct

because 1/n^3 converges

(5)

Correct

because 1/n^2 converges

(6)

Correct

because 1/n^2 converges

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.