**Section 10.4.21** **Topic: Integral Test for Convergence or Divergence of a Series** **Problem Statement:** Use the Integral Test to determine the convergence or divergence of the following series, or state that the test does not apply. \[ \sum_{k=3}^{\infty} k \, e^{-2k^2} \] **Instructions:** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. **Choices:** - **A.** The series converges. The value of the integral \(\int_{3}^{\infty} x \, e^{-2x^2} \, dx\) is \_\_\_. *(Type an exact answer.)* - **B.** The series diverges. The value of the integral \(\int_{3}^{\infty} x \, e^{-2x^2} \, dx\) is \_\_\_. *(Type an exact answer.)* - **C.** The Integral Test does not apply. **Further Instructions:** Click to select and enter your answer(s) and then click Check Answer.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Section 10.4.21**

**Topic: Integral Test for Convergence or Divergence of a Series**

**Problem Statement:**
Use the Integral Test to determine the convergence or divergence of the following series, or state that the test does not apply.

\[ \sum_{k=3}^{\infty} k \, e^{-2k^2} \]

**Instructions:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

**Choices:**

- **A.** The series converges. The value of the integral \(\int_{3}^{\infty} x \, e^{-2x^2} \, dx\) is \_\_\_.
  
  *(Type an exact answer.)*

- **B.** The series diverges. The value of the integral \(\int_{3}^{\infty} x \, e^{-2x^2} \, dx\) is \_\_\_.
  
  *(Type an exact answer.)*

- **C.** The Integral Test does not apply.

**Further Instructions:**
Click to select and enter your answer(s) and then click Check Answer.
Transcribed Image Text:**Section 10.4.21** **Topic: Integral Test for Convergence or Divergence of a Series** **Problem Statement:** Use the Integral Test to determine the convergence or divergence of the following series, or state that the test does not apply. \[ \sum_{k=3}^{\infty} k \, e^{-2k^2} \] **Instructions:** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. **Choices:** - **A.** The series converges. The value of the integral \(\int_{3}^{\infty} x \, e^{-2x^2} \, dx\) is \_\_\_. *(Type an exact answer.)* - **B.** The series diverges. The value of the integral \(\int_{3}^{\infty} x \, e^{-2x^2} \, dx\) is \_\_\_. *(Type an exact answer.)* - **C.** The Integral Test does not apply. **Further Instructions:** Click to select and enter your answer(s) and then click Check Answer.
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