Download Review Ch8.1 8.2 and 8.3

Calculus BC
REVIEW Ch 8.1, 8.2, and 8.3
(Based on homework assignments).
Calculators OK!!!
1. Write the first five terms of the sequence. an =
3n
n!
2. Write the first five terms of the recursively defined sequence. a1 = 32, ak +1 =
3. Use a graphing utility to graph the first ten terms of the sequence. an =
1
ak
2
2
n
3
(2n − 1)!
(2n + 1)!
Determine the convergence or divergence. If the sequence converges, then find its
3n 2 − n + 4
limit. an =
2n 2 + 1
1
2
3
4
Write an expression for the nth term of the sequence.
,
,
,
,...
2 ⋅3 3⋅ 4 4 ⋅ 5 5⋅ 6
Determine whether the sequence is monotonic. Discuss the boundedness of the
1
sequence. an = 4 −
n
1 1 1 1
Find the first five terms of the sequence of partial sums. 1 + + + + ...
4 9 16 25
Graph the following sequence of partial sums, then determine the sum of the series.
4. Simplify the ratio of factorials.
5.
6.
7.
8.
9.
∞
91
∑
 
n =0 4  4 
n
∞
10. Verify that the infinite series converges.
1
∑ n(n + 1)
n =1
1 1
11. Find the sum of the convergent series. 3 − 1 + − + ...
3 9
12. Express the repeating decimal as a geometric series and write its sum as the ratio of
two integers. 0.4
∞
3n − 1
13. Determine the convergence or divergence of the series. ∑
n =1 2n + 1
∞
14. Determine the convergence or divergence of the series.
∑ (1.075)
n
n =0
∞
15. Use the Integral Test to determine the convergence or divergence of the series.
∑e
n =1
16. Use the Integral Test to determine the convergence or divergence of the series.
ln 2 ln 3 ln 4 ln 5 ln 6
+
+
+
+
+ ...
2
3
4
5
6
−n
∞
17. Determine the convergence or divergence of the p-series.
∑
n =1
5
1
n
18. Determine the convergence or divergence of the p-series.
1
1
1
1
1+
+
+
+
+ ...
2 2 3 3 4 4 5 5
19. Approximate the sum of the convergent series using the indicated number of terms.
∞
1
Include an estimate of the maximum error for your approximation. ∑ 2
Use ten
n =1 n + 1
terms.
∞
20. Find N such that RN ≤ 0.001 for the convergent series.
∑e
n =1
−5 n