METU Math 118 Calculus II Recitation Problems - Week 07
1. Determine the convergence of the following series.
(a) โ
X
n=0 ๎n+ 1
n+ 2๎n
(b) โ
X
n=3
1
nln nโnln n
(c) โ
X
n=1
n!
2n2
(d) โ
X
n=1
4ฯn+n2
e2n+ 1 (e) โ
X
n=0
4
โ2n3+n
3
โ1+3n5(f) โ
X
n=1
2n
nโn
2. Determine whether the following series converge absolutely, converge conditionally, or diverge.
(a) โ
X
n=1
(โ1)n
n3/2+ ln(n)
(b) โ
X
n=1
(โ1)n+1 ne
1 + nฯ
(c) โ
X
n=1
cos(nฯ)(n3โ3n2+ 7)
2n3+ 13 .
3. Find the smallest integer nthat ensures that the partial sum snapproximates the sum of the series
โ
X
n=1
(โ1)nโ1
(2n)! with |error|=|sโsn|<0.001.
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