Find the exact sum of the convergent series n0suminfin723n

Question

1. Find the exact sum of the convergent series _n=0∑^∞7(2/3)ⁿ.

2. True or false: The series _n=0∑^∞(10/5ⁿ) is divergent. Justify your answer.

3. Use the Integral Test to determine the convergence or divergence of the series:

_n=0∑^∞n/(n² +1)³

4. True or false: The series _n=2∑^∞(-1)ⁿ/3ⁿ is divergent. Justify your answer.

5. Use the Ratio Test to determine the convergence or divergence of the series:

_n=1∑^∞(n!/(n²)(8ⁿ))

6. Determine the convergence or divergence of the series using any appropriate test from this chapter. Show all work and identify the test used.

_n=1∑^∞((-1)ⁿ3/5n²)

7. Determine the convergence or divergence of the series using any appropriate test from this chapter. Show all work and identify the test used.

_n=1∑^∞4n/9n+5

8. Find the Maclaurin polynomial of degree 4 for the function f (x) = e^3x.

9. Find the interval of convergence of the power series _n=1∑^∞((-1)ⁿ(x-4)ⁿ/(n²)(3ⁿ)). (Be sure to check for convergence al the endpoints of the interval.)

10. Find a geometric power series for the function f (x) = (6/2-x), centered at 0.