Review Sheet 1 Math H162

[n]
means the topic is found on acetate n.

Theory that might be on Midterm I
is marked by asterisks *******. Four
items are marked. One of them will
be on the exam.

To the exam you may bring one 8-1/2 x 11
sheet of paper on which are written the various convergence and divergence
teats.

**Bold face indicates material that will not
be on Midterm I, but will be on Midterm II. This includes the material on power series.**

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**Tools**

Integration
techniques, including integration by parts

Least
Upper Bound axiom for the real number system

Triangle
inequality [9.1]

L'Hopital's
rule [25.0]

** **

**Definitions** (know them and be able to write them correctly)

Infinite series [2]

Infinite sequence [2]

Limit of a sequence [8.1 – 8.3]

Partial sums of a series [3, 6.1, 7]

Convergent series [6.1, 7]

Properties of sequences [9.2, 16 - 17]

Properties of series [19, 23.0, 24, 34 – 35, 53, 54.0, 55 - 59]

Divergent series [6.2, 7]

Absolutely convergent series [51]

Conditionally convergent series [51]

Sum of a series [3, 6.1, 7, 23.0]

**Power series [60 – 61]**

**Properties of power series [63.0 – 63.1]**

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**Examples**

** **

** I**nfinite series
[2, 55 - 59]

Infinite
sequences [2]

Telescoping
series [4]

Power
series [bottom of 5]

Convergent
series [4, 45]

Divergent
series [6.2]

Harmonic
series [10]

Geometric
series [11]

p-series
[25.1, 31]

**power
series [62.0]**

** **

**Theorems--with
proofs**

*******Adding sequences
[9.1 – 9.2]

*******Convergence and divergence of geometric series,
depending on the ratio [11, 40.8]

*******If an increasing infinite sequence has an upper bound,
then it converges [12.1 – 14]

*******If a series is absolutely convergent then it is
convergent. [52]

**Theorems--no
proofs** (know what they mean and be able to
state and use them correctly)

Theorems on
subtraction of sequences and multiplication and division of sequences, both by
a constant and by another sequence
[9.2]

Comparison test [20,
22, 25.1, 30]

p-series [25.1]

Limit comparison
test [26 - 30]

Integral test [37.0 – 37.2]

Ratio test [41 - 42]

Root test [46 – 47.2]

Alternating series
test [49]

**Calculations**

Sum of a finite geometric series

Partial fractions

Telescoping
series [4]

**Notation**

Notation used in writing down limits
and series [8.1]

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