METU Math 118 Calculus II Recitation Problems - Week 07
1. Determine the convergence of the following series.
(a) ∞
X
n=0 n+ 1
n+ 2n
(b) ∞
X
n=3
1
nln n√nln n
(c) ∞
X
n=1
n!
2n2
(d) ∞
X
n=1
4πn+n2
e2n+ 1 (e) ∞
X
n=0
4
√2n3+n
3
√1+3n5(f) ∞
X
n=1
2n
n√n
2. Determine whether the following series converge absolutely, converge conditionally, or diverge.
(a) ∞
X
n=1
(−1)n
n3/2+ ln(n)
(b) ∞
X
n=1
(−1)n+1 ne
1 + nπ
(c) ∞
X
n=1
cos(nπ)(n3−3n2+ 7)
2n3+ 13 .
3. Find the smallest integer nthat ensures that the partial sum snapproximates the sum of the series
∞
X
n=1
(−1)n−1
(2n)! with |error|=|s−sn|<0.001.
1