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Review Sheet for Third Exam
Mathematics 2300
November 15, 2006
The exam will cover all of Chapter 10.
No calculators of any kind will be allowed.
Definitions to know:
When we say know the definitions, this is a good indicator that you should know the defi-
nitions. Remember how you did with the definition of the limit on the last exam? Not so
great, huh? Do better this time.
. Limit of a sequence: The sequence {an} converges to L if, for any ? > 0, there is an
integer N such that |an ?L| < ? for every n ? N.
Example: limn?? n2+1n2 = 1 since for any ? > 0, we can choose N to be the first integer
above 1??. Then if n ? N, we will have |an ?L| = | 1n2| < ?.
. (Strictly) increasing: The sequence {an} is increasing if a1 ? a2 ? a3 ? ···. It is
strictly increasing if a1 < a2 < a3 < ···. It is eventually increasing if deleting finitely
many terms makes it an increasing sequence.
Examples: {2n+(?1)n} = 1,3,3,5,5,7,7,··· is increasing but not strictly increasing.
{n2} = 1,4,9,16,··· is strictly increa...

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