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What sigma notation is and how to use it
Writing series in sigma notation
Go from sigma notation to expansion of terms
Find the sum

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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 of negative numbers using series
Use Euler's Formula
Write natural logarithm of negative number
Fibonacci Series and why it's important

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Use mathematical induction to prove the validity of mathematical statements.
Use it for a series/sum 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 equation (use Paschal's triangle's numbers. The x will start with the original exponent and descend until zero. The y will start with zero and ascend until the original exponent).
Find a specific term of a binomial (n!/r!(n-r)! x^n-r y^r

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Write a complex number (use Euler's formula)
Approximate the value of e^n (use the first five terms of the exponential or trigonometric series)

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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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Use parentheses
Make sure it is in the correct mode.

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Only use S=a1/(1-r) for an infinite sum, not a finite sum.

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Remember that n=the original exponent and that r= one less than the term number when using the theorem.

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

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Do not skip over the n=k step.
When beginning the third step, just bring down the term on the right side (do not add k+1 yet).

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

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Get sigma on the calculator for finite sums: Math button, then Zero.
Don't forget parentheses!

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You cannot evaluate a natural log of a negative number as a complex number on a calculator. You have to use Euler's Formula.