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MATH 2B Study Guide - Midterm Guide: Squeeze TheoremPremium


Department
Mathematics
Course Code
MATH 2B
Professor
All
Study Guide
Midterm

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Section 11.1 - Sequences
What is a sequence?
A sequence is a list of numbers
,,,,,.... ..
You can easily tell there are patterns to certain sequences
Defining these patterns
Explicitly
= ()
You can just say that the value of is just the function ()
Recursively
= ()
Where =  
Example #1
Define the sequence: 1, 2, 3, 4, 5, 6…
Recursively
= () + 1, where = 1
Because each number is one more than the last, we can set to be the
sum of the previous () and 1
Explicitly
=
We can prove these by plugging in the numbers and checking
= 1, = 2, = 3, . ..
Example #2
Define the sequence: 3, 5, 7, 9, 11, 13, 15…
Recursively
= () + 2, where = 3

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Each value is 2 more than the last
Explicitly
= 2 + 1
Because we can see that each is 2 + 1
= 2(1) + 1 = 3, = 2(2) + 1 = 5, = 2(3) + 1 = 7
Example #3
1, 2, 4, 8, 16, 32…
Recursively
= 2(), where = 1
Explicitly
= 2
This one is slightly more difficult to see outright, but if we notice
something, it’s that the numbers are all being multiplied by 2 as it goes
along, and so we conclude that it would be 2
Example #4
1, 4, 9, 16, 25, 36…
Recursively
=  + (21), where = 1
Explicitly
=
Because the numbers are simply squared
Types of Sequences
Arithmetic
These would be examples 1 and 2
These are patterns involving adding some same number every single time
,+,+ 2,+ 3. ..
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