MAT A37H
Summer 2011
Assignment # 11
You will NOT submit any of these questions but you should make sure that you are able
to answer them. Your TA may present solutions for a nonempty subset of these exercises
during TUTORIAL in the week of Aug. 1st and Aug. 8th).
STUDY:
Chapter 22 (BMCT) and Chapter 23 (pg 471

482 only, and excluding the
Cauchy Criterion and all theorems dealing with ’absolute convergence’)
HOMEWORK PROBLEMS:
1. Show the sequence deﬁned by
a
1
= 2,
a
n
+1
=
1
2
(
a
n
+ 6) if
n
≥
1, is convergent.
2. Determine whether the series
∞
X
n
=1
±
1
√
n

1
√
n
+ 1
²
is convergent or divergent. If it is
convergent, then ﬁnd its sum.
3. Let
a
n
=
2
n
3
n
+1
.
(a) Determine whether
{
a
n
}
is convergent.
(b) Determine whether
∑
a
n
is convergent.
4. Determine whether the series is convergent or divergent. If it is convergent, then ﬁnd
its sum.
(a) 1 + 0
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 Summer '11
 Katherine
 Math, Convergence, n=1, Dominated convergence theorem

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