Calculus II – Worksheet 13
8.3 More Tests
1. Determine whether the series converges. Clearly state what test(s) is used and how it applies.
(a)
∞ n 2 + n + 1
∞ 1 (c) sin n
n=1
∞ 1
(d) cosn n=1
n5 + n + 1 ∞2n−n
n=2
(b) 3n n=2
2. Determine the convergence or divergence of the following series. Clearly state what test(s) is used and how it applies.
(a)∞n2−1
(c)∞ 1
3n4 +1 ∞ 3
(b) √2n−2 n=2
3. For what values of p is the series ∞ n=2
nlnn ∞sin2n
n=1
n=2
(d) n2
1 n(ln n)p
n=2
convergent?