Calculus Exam: Series Convergence/Divergence (9.1-9.6)
Part 1: Non-Calculator
Name: ______Date ______
1. Write the first three terms of the sequence.
a. /b. /
c. /
d. /
e. /
2. Find the positive values of for which the series converges.
a. / converges forb. / diverges only at
c. / converges for
d. / converges for
e. / converges for
3. Find the sum of the convergent series.
a. /b. /
c. /
d. /
e. /
4. 1998 #18
5. Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.
a. / The sequence diverges.b. / The sequence converges to 4.
c. / The sequence converges to 3.
d. / The sequence converges to 1.
e. / The sequence converges to 0.
6. Find the sum of the convergent series.
a. /b. /
c. /
d. /
e. /
7. 1997 #20
8. Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.
a. / both diverges; p-series and diverges; Integral Testb. / converges; p-series
c. / converges; Ratio Test
d. / diverges; p-series
e. / diverges; Integral Test
9. Consider the series.
Review the Alternating Series Test to determine which of the following statements is true for the given series.
a. / Since for some n, the series diverges.b. / Since cannot be shown to be true for all n, the Alternating Series Test cannot be applied.
c. / The series converges.
d. / Since cannot be shown to be true for all n, the series diverges.
e. / Since , the series diverges.
10. 2003 #10
11. Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.
a. /b. /
c. /
d. /
e. /
12. Use the Ratio Test to determine the convergence or divergence of the series .
a. /b. /
c. Ratio test inconclusive
13. Find all values of x for which the series converges.
a. /b. /
c. /
d. /
e. /
Calculus Exam: Series Convergence/Divergence (9.1-9.6)
Part 2: Calculator
Name: ______Date ______
1. Write the first five terms of the sequence of partial sums.
a. /b. /
c. /
d. /
e. /
2. Find the positive values of for which the series converges.
a. / The series converges for .b. / The series converges for .
c. / The series diverges for all positive values of .
d. / The series converges for .
e. / The series converges for .
3. The series is a convergent series. Use Theorem 9.15 to determine the number of terms required to approximate the sum of this series with an error less than 0.001.
a. /b. /
c. /
d. /
e. /
4. 1997 #14
5. 1997 #76
6. Find the sum of the convergent series
a. /b. /
c. /
d. /
e. /
7. 1998 #76
8. Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.
a. / both diverges; Ratio Test and diverges; Theorem 9.9 (nth Term Test for Divergence)b. / converges; Integral Test
c. / diverges; Theorem 9.9 (nth Term Test for Divergence)
d. / converges; p-series
e. / diverges; Ratio Test
9. 1998 #84
10. 2003 #24
11. Use the Ratio Test to determine the convergence or divergence of the series.
a. / divergesb. / converges
c. / Ratio Test inconclusive
12. 2003 #22