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Writing a series in Sigma Notation
Expanding terms to find the sum
Using Sigma Notation

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Pascal's triangle
Expanding a binomial (all terms)
Finding a particular term in binomial expansion.

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Approximate e^x, trigonometric values, and logarithms using series
Euler's Formula
Natural log of a (-) number to a complex number
Fibonacci Series

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proving validity of statements
divisibility definition p=qr
used for both series and divisibility statements

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Expand a series from sigma notation (plug in the first n value to the formula and keep increasing by 1).
Find a finite sum using calculator.
Find an infinite sum using formula  S=a1/(1-r)
Go from a series to the sigma notation.

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Expand a binomial
1) Use Pascal's Triangle, using the number of terms in the binomial to identify which row in the triangle to use
2) Plug in the values found in the corresponding row
3) Simplify if possible

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Approximate e^x by using the first three terms of an exponential series.
1) Plug in the value of x for all n
2) add the first three terms together (do not round until the final solution)

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Series proof.
Divisibility proof.
Use 3 steps of induction.
Show n=1 works.
Assume n=k works.
Show n=k+1 works.

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Remember that the bottom number is the term that is started with, not the number that is started with.

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Check which row is being used for the corresponding binomial.

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On e^x problems, don't round along the way.

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when solving n=k+1 remember to put parenthesis
don't forget to add the second term to both sides of the statement
remember to write what t equals; t always equals and integer

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Get sigma on calculator for finite sums: Math button, then press Zero

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put parenthesis around terms when necessary
put exponents outside of parenthesis if necessary
use the ! button by going to "math" then "prob" then press #4

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Make sure to use parentheses properly

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don't forget to put parenthesis when necessary
most calculating does not require a calculator