Select the FIRST correct reason why the given series converges. Select the FIRST

Question

Select the FIRST correct reason why the given series converges.

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. Ratio Test ___ 1. displaystyle sum_{n=1}^infty (-1)^n frac{sqrt{n}}{n +2} ___ 2. displaystyle sum_{n=1}^infty frac{(-1)^n}{2 n + 7} ___ 3. displaystyle sum_{n=1}^infty frac{2 (6)^n}{10^{2n}} ___ 4. displaystyle sum_{n=1}^infty frac{(n+1)}{10^{2n}} ___ 5. displaystyle sum_{n=1}^infty frac{n^2}{n^4 -2} ___ 6. displaystyle sum_{n=1}^infty frac{sin^2 (7 n)}{n^2}

Explanation / Answer

1.) This series converges by the alternating series test.

2.) This series converges by the alternating series test.

3.) This is a convergent geometric series.

4.) This is convergent with the ratio test.

5.) You can use the limit comparison test for this series.

6.) YOu can use the comparison test for this series.

1.) D

2.) D

3.) A

4.) E

5.) C

6.) C

Those are your answers.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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